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visit MIT OpenCourseWare at ocw.mit.edu. PROFESSOR: OK, in

that case we can jump into the early universe. So on the opening slide

here I have a picture of the Planck satellite,

which is a satellite that was launched a few years

ago dedicated to measuring the cosmic background radiation. Cosmic background

radiation is really our biggest clue for the

early history of the universe. The Planck satellite is

actually the third satellite to go up completely dedicated to

measuring the cosmic background radiation. The first was called COBE

and then WMAP and now Planck. Planck is still in orbit. It actually is finished

with its data-taking, although it’s

nowhere near finished with the analysis of that data. So they made one major

data release last March, and there are still very

important pieces of their data that I haven’t looked at yet. And we’ll be talking

more about what exactly these satellites see. Onward. I want to begin by talking about

the standard Big Bang, which will in fact be the main

focus of this course. We’ll probably spend about 2/3

of the course or so talking about the standard Big

Bang and then move on to topics like inflation. That actually is, I think,

a very sensible balance, because as you’ll see once we

get under studying inflation, it’s a fairly straightforward

thing once you know the basic equations coming

out of standard cosmology. So I think spending about

2/3 of the term or so on the conventional cosmology

before we get to inflation is very sensible, because that

will set up all the principles that we’ll be using

later to discuss more advanced topics like inflation. The conventional Big Bang

model is basically the theory that the universe as

we know it began some 13 to 14 billion years ago. And now we even have a

pretty precise number to replace this 13

to 14 billion years. This is based on

the Planck satellite combined with a few other

pieces of information. The number is 13.82 billion

years, plus or minus 0.05. So it’s pretty well

pinned down now, the age of the universe

since the Big Bang. I should add, though, I put

in the qualifier “the universe as we know it.” What that really means is

that I want to leave it out, because we don’t really

know that the universe began with what we call the Big Bang. So we have a very good

picture of the Big Bang, and we’re very confident

that it happened and that we understand

what it looked like. But whether or not

anything came before it is a much more open

question which I think is really completely open. I think we should not act like

we know that the universe began with the Big Bang. And in fact later at the

very end of the course when we discuss some of the

implications of inflation and the multiverse,

we’ll see that there are strong suggestions that the

Big Bang was perhaps not really the beginning of

existence, but really just the beginning of

our local universe, often called a pocket universe. OK. In any case, what the

Big Bang theory tells us is that at least our

region of the universe 13.82 billion years ago was an

extremely hot, dense, uniform soup of particles, which in the

conventional standard Big Bang model filled literally

all of space. And now we certainly believe

it filled essentially all the space that we have

access to uniformly. Now I should point

out that this is contrary to a popular cartoon

image of the Big Bang, which is just plain wrong. The cartoon image

of the Big Bang is the image of a small egg

of highly dense matter that then exploded and spewed

out into empty space. That is not the scientific

picture of the Big Bang. And the reason is not

because it’s illogical. It’s hard to know what’s logical

or illogical in this context. But simply based on

what we see, if there was a small egg that

exploded into empty space, you would certainly

expect that today you would see something different

if you were looking toward where the egg was versus looking

the opposite direction. But we don’t see any

effect like that. When we look around

the sky, the universal looks completely uniform, on

average, in all directions to very high degree of accuracy. I’ll talk a little bit

more precisely later. So we don’t see any sign of an

egg having happened anywhere. Rather the Big

Bang seems to have happened everywhere uniformly. OK. The Big Bang describes a

number of important things, and we’ll be talking about this

more as the course goes on. It describes how the early

universe expanded and cooled– and will be spending a fair

amount of time understanding the details behind those words. The point is that

the Big Bang really is a very precise model based

on very simple assumptions. You basically assume

that the early universe was filled by a hot gas

in thermal equilibrium. And that this gas was

expanding and being pulled back by gravity. And from those simple ideas

you can really calculate– and we’ll learn

how to calculate– how fast the universe would

have been expanding at any given instant of time, what the

temperature would have been at any given instant of time,

what the density of matter would have been at

any instant of time. So all the details

really can be calculated from some rather

simple ideas, and we’ll have fun exploring that. The Big Bang also talks

about how the light chemical elements formed. And that actually

is the main topic of Steve Weinberg’s book

“The First Three Minutes.” Because that was more or less

the time period during which the chemical elements formed. It turns out that most of

the elements in the universe did not form in the Big

Bang, but formed much later in the interior of stars. And those elements are

then strewn out into space in supernova explosions and

collected into later generation stars, of which our

sun would be one. So the stuff that we’re made

out of was actually not produced in the Big Bang, but

rather was produced in the interior of some distant

star that exploded long ago. And maybe many

stars, whose material collected to form

our solar system. Nonetheless, most of the matter

in the universe– as opposed to most of the different

kinds of elements– did form in the Big Bang. Most of the matter

in the universe is just hydrogen and helium. About five different isotopes

of hydrogen, helium, and lithium were primarily formed

in the Big Bang, and because we do have this

detailed picture of the Big Bang that we’ll

be learning about, it’s possible to

actually calculate the predicted abundances of

those different isotopes. And the predictions agree very

well with the observations. And this is certainly one

of the major confirmations we have that this picture

of the Big Bang is correct. We can predict what the

abundance of helium-3 should be, and we measure

it, and it agrees. It’s rather marvelous. Finally– and this

subject we’re not going to talk about

much because it goes beyond the

level of complexity that the course

is going to have– but finally the Big

Bang does discuss how the matter ultimately

congealed to form stars, galaxies, clusters of galaxies. We’ll talk about

that a little bit, but we won’t really

follow that very far. That is still in principle

a work in progress. People do not understand

everything about galaxies. But the general picture

of that– it started out with an almost uniform

universe, and then the lumps congealed to form the

galaxies and the structures– we say certainly seems

to be a working picture. And one can understand

a lot about the universe from this very simple picture. OK what I want to

talk about next is what the conventional

Big Bang theory does not talk about, where new ideas

like inflation come in. First of all, the

conventional Big Bang theory does not say anything about

what caused the expansion. It really is only a theory

of the aftermath of a bang. In the scientific

version of the Big Bang, the universe starts with

everything already expanding with no explanation of how

that expansion started. That’s not part of

the Big Bang theory. So the scientific version

of the Big Bang theory is not really a

theory of a bang. It’s really the theory of

the aftermath of a bang. In addition, and maybe

in a similar vein, the conventional

Big Bang theory says nothing about where all

the matter came from. The theory really assumes that

for every particle that we see in the universe

today, there was at the very beginning at

least some precursor particle, if not the same particle,

with no explanation of where all those particles came from. In short, what I like to say is

that the Big Bang says nothing about what banged,

why it banged, or what happened

before it banged. It really has no

bang in the Big Bang. It’s a bangless theory,

despite its name. Inflation, it turns out,

fills in possible answers, very plausible answers, for

many of these questions. And that’s what I’ll

be talking about mainly for the rest of today. And as I said, in

terms of the course, it’s where we’ll be aiming

to get about 2/3 of the way through the semester. What is cosmic inflation? It’s basically a

minor modification, in terms of the overall

scheme of things, of the standard Big Bang theory. And the best word to describe

it is a word that I think was invented by

Hollywood– inflation is a prequel to the

conventional Big Bang theory. It’s a short description

of what happened before, immediately before,

the Big Bang. So inflation really

is an explanation of the bang of the

Big Bang in the sense that it does provide a

theory of the propulsion that drove the universe into this

humongous episode of expansion which we call the Big Bang. And it does it in

terms of something that I like to think of

as a miracle of physics. When I use the word “miracle”

in this context– referring to a miracle in the

scientific sense– simply something that’s

so surprising that I think it merits being called a miracle

even though it’s something that’s a part of

the laws of physics. There are just a few features

of the laws of physics that are actually

crucial to inflation– I’ll be talking

about two of them– which I consider miracles

simply because– well, mainly because when I

was an undergrad nobody talked about them at all. They were just not

part of physics then, even though they really were. They just weren’t

parts of physics people noticed and talked about. So the miracle of physics

I’m talking about here is something which

actually is known since the time of Einstein’s

general relativity– that gravity is not

always attractive. Gravity can act repulsively. And Einstein introduced

this in 1916, I guess, in the form of what he called

his cosmological constant. And the original

motivation of modifying the equations of general

relativity to allow this was because Einstein thought

that the universe was static. And he realized that

ordinary gravity would cause the universe to

collapse if it were static. It couldn’t remain static. So he introduced this

cosmological constant term to balance the overall

attraction of ordinary gravity to be able to build a static

model of the universe. As you’ll soon be learning,

that’s dead wrong. That’s not what the

universe looks like at all. But the fact that

general relativity can support this

gravitation repulsion, still being consistent with

all the principles that general relativity

incorporates, is the important

thing which Einstein himself did discover

in this context. And inflation takes advantage

of this possibility, within the context of

general relativity, to let gravity be the

repulsive force that drove the universe into

the period of expansion that we call the Big Bang. And in fact when one

combines general relativity with conventional ideas

now in particle physics, there really is a

pretty clear indication, I should say– not quite a

prediction– but a pretty clear indication that at very

high energy densities, one expects to find states of

matter which literally turn gravity on its head and cause

gravity to become repulsive. In terms of the details which

we’ll be learning about more later, what it takes to

produce gravitational repulsion is a negative pressure. According to general

relativity, it turns out– and we’ll be talking more about

this later– both pressures and energy densities can

produce gravitational fields. Unlike Newtonian physics,

where it’s only mass densities that produce

gravitational fields. And the positive

pressure produces an attractive

gravitational field, which is what you would

probably guess if somebody just asked you to guess. Positive pressures are

sort of normal pressures, and attractive gravity

is normal gravity. So normal pressures

produce normal gravity. But it is possible to

have negative pressures, and negative pressures

produce repulsive gravity. That’s the secret of what

makes inflation possible. So inflation proposes that

at least a small patch of this repulsive

gravity material existed in the early universe. We don’t really

know exactly when in the history of the

universe inflation happened, which is another way of

saying we don’t know exactly at what energy scale

inflation happened. But a very logical,

plausible choice– I don’t know if logical is

the right word, but plausible is a good word–

very plausible choice for when inflation

might have happened, would be when the energy

scales of the universe where at the scale of grand

unified theories. Grand unified theories– we’ll

talk about a little bit later– are theories which

unify the weak, strong, and electromagnetic

interactions into a single unified interaction. And that unification occurs at

a typical energy of about 10 to the 16 GeV, where GeV,

in case you don’t know, is about the mass–

or the energy equivalent of the

mass– of a proton. So we’re talking

about energies that are about 10 to the 16 times the

equivalent energy of a proton mass. And at those energies we

think that these states that create repulsive gravity

are very likely to exist. And if that happened

at that scale, the initial patch

would only have to be the ridiculously

small size of about 10 to the minus 28

centimeters across to be able to lead ultimately

to the creation of everything that we see on the vast

scale at which we see it. The patch certainly does not

have to be the entire universe. And it could in fact

be incredibly rare, because one thinks that outside

of that patch essentially nothing will happen interesting. So we expect that the

universe that we observe today would be entirely the

consequence of such a patch. The gravitational

repulsion created by this small patch of

repulsive gravity material would be then the driving

force of the Big Bang, and it would cause the region to

undergo exponential expansion. And by exponential expansion,

as you probably know, it means that there’s a

certain doubling time, and if you wait the same amount

of time it doubles again. If you wait the same amount

of time, it doubles again. And because these doublings

build up so dramatically, it doesn’t take very much time

to build the whole universe. In about 100 doublings,

this tiny patch of 10 to the minus

28 centimeters can become large enough

not to be the universe, but to be a small marble

size region, which will then ultimately become

the observed universe as it continues to coast

outward after inflation ends. So the doubling time

would be incredibly small if this was all happening

at the grand unified theory set of numbers– 10 to the

minus 37 seconds, which is pretty fast. The patch would

expand exponentially by at least a factor of about 10

to the 28, which as I mentioned takes only about 100

doublings, and could expand to be much more. There’s no cut off there. If there’s more

expansion than we need to produce our

universe, it just means that the patch of

universe that we’re living in is larger than we see. But that’s OK. Everything that we see looks

uniform as far as we can see, and how much there is

beyond that we really just have no way of knowing. So larger amounts

of inflation are perfectly consistent

with what we see. The amount of time it would

take would only be about 10 to the minus 35 seconds,

which is just 100 times 10 to the minus 37 if you can do

that complicated arithmetic in your head. And the region that’s destined

to become our presently observed universe at

the end of inflation would have been only about the

size of a marble– about one centimeter or so across. Now what ends

inflation is the fact that this repulsive gravity

material is unstable. So it decays, using the

word decay in the same sense that a radioactive

substance decays. It doesn’t necessarily

mean exactly that it rots like

an apple decays, but it means that it turns

into other kinds of material. And in particular, it

turned into material which is no longer

gravitationally repulsive. So the gravitational repulsion

ends, and in fact the particles produced by this

energy that’s released at the end of inflation

become the hot soup of the conventional Big Bang. And this is where

the prequel ends, and the main feature begins–

the conventional Big Bang theory. The role of inflation is just

to set up the initial conditions for the conventional

Big Bang theory. Now there’s a

little caveat here. Inflation ends because

the material is unstable, but it only ends

almost everywhere, not quite everywhere. And this is basically the

way exponentials work. And we’ll come back to this

when we talk about the late time behavior and the idea

of eternal inflation. This repulsive gravity

material decays, but it decays like a radioactive

substance– which is also an exponential– as a half life. But no matter how many

half lives you wait, there’s still a tiny little bit,

a tiny fraction that remains. And that turns out to be

important for the idea that in many cases inflation

never completely ends. We’ll come back to that. So I want to talk more

about what goes on during this exponential

expansion phase. There’s a very peculiar

feature of this inflation– this exponential

expansion driven by repulsive gravity– which

is that while it’s happening, the mass density

or energy density of the inflating material– this

repulsive gravity material– does not decrease. You would think that if

something doubled in radius, it would multiply by a

factor of eight in volume. You would think the energy

density would go down by a factor of eight. And that certainly happens

for ordinary particles. It’s certainly what

would happen if you had a gas, an ordinary

gas, that you just allowed to expand

by a factor of two in radius– the density would

go down by a factor of eight with volumes of

cubes of distances. But this peculiar repulsive

gravity material actually expands at a constant density. Now that sounds like it must

violate conservation of energy, because it really does mean

that the total amount of energy inside this expanding

volume is increasing. The energy per volume

is remaining constant, and the volume is getting

bigger and bigger exponentially. So the claim is that I’ve not

gone crazy, that this actually is consistent with the laws

of physics as we know them. And that it is consistent

with conservation of energy. Conservation of energy really is

a sacred principle of physics. We don’t know of anything

in nature that violates this principle of

conservation of energy, that energy ultimately cannot

be either made or destroyed, that the total amount of

energy is basically fixed. So it sounds like there’s

a contradiction here. How do we get out of it? What’s the resolution? Well, this requires my

second miracle of physics. Energy– it really

is exactly conserved. I’m not going to tell you

about any miracles which changed that. But the catch here is

that energies are not necessarily positive. There are things that

have negative energies. And in particular, the

gravitational field has a negative energy. This statement by the way is

true both in Newtonian physics and in general relativity. We’ll prove it later. I might just say

quickly if some of you have learned in an E&M course

how to talk about and calculate the energy density of an

electrostatic field– probably many of you have,

maybe all of you have– the energy density

of an electrostatic field is a constant times the square

of the electric field strength. And you can prove that

energy is exactly the energy that you need to

put into a system to create an electric field

of a given configuration. If you think about

Newton’s law of gravity and compare it

with Coulomb’s law, you realize that it

really is the same law, except they have a different

constant in front of them. They’re both inverse

square laws in proportion to the two charges, where

in the case of gravity it’s the masses that

play the role of charges. But they have opposite signs. Two positive charges, as we

all know we tell each other, two positive masses

attract each other. So in fact the

very same argument which allows you to calculate

the energy density of a Coulomb field can allow you to

calculate the energy density of a Newtonian

gravitational field– still sticking to Newtonian

physics– and this change in sign of the force

just carries through. It changes the signs of all

the work that’s being done, and you get the

negative answer that is the correct answer

for Newtonian gravity. The energy density of a

Newtonian gravitational field is negative. And the same is true

in general relativity in a more subtle way. So what that means in terms

of conservation of energy is that we can have more

and more matter, more and more energy building up in

the form of ordinary matter– which is what happens during

inflation– as long as there’s a compensating amount

of negative energy that’s created in the

gravitational field which is filling this ever

larger region of space. And that’s exactly what

happens in inflation. The positive energy of this

repulsive gravity material which is growing and

growing in volume is precisely canceled

by the negative energy of the gravitational field

that’s filling the region. So the total energy

does remain constant, as it must, and there’s

certainly a good possibility that the total energy

is exactly zero. Because everything

that we know of is at least consistent

with the possibility that these two

numbers are exactly equal to each other or

something very close. Schematically, the picture

is that if one thinks about the total energy

of the universe, it consists of a huge positive

amount in the form of matter and radiation– the

stuff that we see, the stuff that we

normally identify the energy of– but there’s

also a huge negative amount of energy in the gravitational

field that fills the universe. And as far as we

can tell, the sum is at least consistent

with being 0. In any case, what

happens during inflation is the black bar goes up

and the red bar goes down. And they go up and

down by equal amounts. So certainly what happens during

inflation conserves energy, as anything consistent with the

laws of physics that we know of must conserve energy. I just remembered I was planning

to turn out these blackboard lights. It probably makes it a

little more comfortable to watch the screen. OK. So, onward. I want to talk some about

the evidence for inflation. So far I’ve described

what inflation is– and I’m sort of done describing

what inflation is for today. As I said, we’ll be coming

back and talking about all this during the coming semester. Now let’s move on to

discuss some of the reasons why we think that our universe

may very likely have actually undergone this process

called inflation I was just telling you about. So there are three things

I want to talk about. The first of which is the

large scale uniformity of the universe. Which is related to what I

told you at the beginning, that if you look out

in different directions in the universe, it really looks

the same in all directions. And the object that can

be measured with the most precision in terms of how

things vary with angle, is the cosmic

background radiation– because we can measure

it from all directions, and it’s essentially

a uniform background. And when that’s been

done, what’s been found is that the radiation is uniform

to the incredible accuracy of about one part in

100,000– which really is a rather spectacular

level of uniformity. So it means the universe really

is rather incredibly uniform. I might mention one proviso here

just to be completely accurate. When one actually just goes

out and measures the radiation, one finds something– one

finds an asymmetry that’s larger than what I just said. One finds an asymmetry

of about 1 part in 1,000, with one direction being hotter

than the opposite direction. But that 1 part in 1,000 effect

we interpret as our motion through the cosmic background

radiation, which makes it look hotter in one

direction and colder in the opposite direction. And the effect of our motion

has a very definite angular pattern. We have no other way of

knowing what our velocity is relative to the cosmic

background radiation. So we just measure it

from this asymmetry, but we’re restricted. We can’t let it

account for everything. Because it has a very

different angular form, we only get to

determine one velocity. And once we determine that,

that determines one asymmetry and you can subtract that out. And then the

residual asymmetries, the asymmetries that we cannot

account for by saying that the Earth has a certain

velocity relative to the cosmic background radiation, those

asymmetries are at the level of 1 part in 100,000. And this is 1 part in

100,000 that we attribute to the universe and not to

the motion of the earth. OK. So to understand

the implications of this incredible

degree of uniformity, we need to say a

little bit about what we think the history of this

cosmic background radiation was. And what our theories

tell us– and we’ll be learning about

this in detail– is that in the

early period– Yes. AUDIENCE: I’m sorry. I’m curious. When they released

WMAP and stuff, did they already subtract

out the relativistic effect? PROFESSOR: Well, the answer

is that they analyze things according to angular

patterns and how they fit different

angular patterns. So in fact, I think they don’t

even report it with WMAP, but it would be what

they would call L equals 1, the dipole term. They analyze the dipole,

quadrupole, octupole, et cetera. So it really does not

contribute at all to anything except that L

equals 1 term, which is one out of 1,800

things that they measure. So basically, I

think they don’t even bother reporting

that one number, and therefore it’s

subtracted out. OK. Do feel free to ask

questions, by the way. I think it’s certainly

a small enough class that we can do that. OK. So what I was about to

say is that this radiation during the early period of the

universe, when the universe was a plasma, the radiation

was essentially locked to the matter. The photons were moving

at the speed of light, but in the plasma there’s

a very large cross section for the photons to scatter

off of the free electrons in a plasma. Which basically means that the

photons move with the matter– because when they’re

moving on their own, they just move a

very short distance and then scatter, and then

move in a different direction. So relative to the

matter, the photons go nowhere during the

first 400,000 years of the history of the universe. But then at about 400,000

years the universe cools enough– this

is all according to our calculations–

the universe cools enough so that the

plasma neutralizes. And when the plasma neutralizes,

it becomes a neutral gas like the air in this room. And the air in this room seems

completely transparent to us, and it turns out

that actually does extrapolate to the universe. The gas that filled the universe

after it neutralized really was transparent, and it means

that a typical photon that we see today in the cosmic

background radiation really has been traveling on

a straight line since about 400,000 years

after the Big Bang. Which in turn means that when

we look at the cosmic background radiation, we’re

essentially seeing an image of what the universe

looked like at 400,000 years after the Big Bang. Just as the light traveling

from my face to your eyes gives you an image

of what I look like. So that’s what we’re seeing–

a picture of the universe at the age of 400,000

years, and it’s bland– uniform to

1 part in 100,000. So the question then

is, can we explain how the universe

to be so uniform? And it turns out that if you–

Well, I should say first of all that if you’re

willing to just assume that the universe started out

perfectly uniform to better than one part in

100,000, that’s OK. Nobody could stop

you from doing that. But if you want to try to

explain this uniformity without assuming that it was

there from the beginning, then within the context of the

conventional Big Bang theory, it’s just not possible. And the reason is that within

the evolution equations of the conventional Big Bang

theory, you can calculate– and we will calculate

later in the course– that in order to smooth things

out in time for it to look smooth in the cosmic

background radiation, you have to be able to move

around matter and energy at about 100 times

the speed of light. Or else you just couldn’t do it. And we don’t know of anything

in physics that happens faster than the speed of light. So within physics as we know it,

and within the conventional Big Bang theory, there’s no way to

explain this uniformity except to just assume that maybe it was

there from the very beginning. For reasons that we

don’t know about. On the other hand, inflation

takes care of this very nicely. What inflation does

is it adds this spurt of exponential expansion to

the history of the universe. And the fact that this

exponential expansion was so humongous

means that if you look at our picture

of the universe before the inflation

happened, the universe would have been vastly smaller

than in conventional cosmology which would not have this

exponential spurt of expansion. So in the inflationary

model there would’ve been plenty of

time for the observed part of the universe to become

uniform before inflation started– when it

was incredibly tiny. And then would become uniform

just like the air in the room here tends to spread out and

produce a uniform distribution of air rather than having

all the air collected in one corner. Once that uniformity

is established on this tiny region,

inflation would then take over and

stretch this region to become large enough

to include everything that we now see,

thereby explaining why everything that we

see looks so uniform. It’s a very simple

explanation, and it’s only possible with

inflation and not within the conventional

Big Bang theory. So, the inflationary solution. In inflationary

models the universe begins so small that uniformity

is easily established. Just like the air in the

lecture hall– same analogy I used– spreads uniformly

to fill the lecture hall. Then inflation

stretches the region to become large enough

to include everything that we now observe. OK. So that’s the first

of my three pieces of evidence for inflation. The second one is something

called the flatness problem. And the question is, why was

the early universe so flat? And the first question

maybe is, what am I talking about when I say

the early universe was flat? One misconception

I sometimes find people getting is that flat

often means two dimensional. That’s not what I mean. It’s not flat like a

two dimensional pancake. It’s three dimensional. The flat in this context

means Euclidean– obeying the axioms of

Euclidean geometry– as opposed to the non-Euclidean

options that are offered by

general relativity. General relativity allows three

dimensional space to be curved. And if we only consider uniform

curvature, which is– we don’t see any

curvature, actually, but– We know with

better accuracy that the universe is uniform

than we do that it’s flat. So imagine in terms of

discussion of cosmology three possible curvatures for

the universe, all of which would be taken to be uniform. Three dimensional curved spaces

are not easy to visualize, but all three of

these are closely analogous to two dimensional

curved spaces, which are easy to think about. One is the closed geometry

of the surface of a sphere. Now the analogy is that the

three dimensional universe would be analogous to

the two dimensional surface of a sphere. The analogy changes the

number of dimensions. But important things get capped. Like for example on the

surface of a sphere, you can easily visualize–

and there’s even a picture to show

you– that if you put a triangle on the

surface of a sphere, the sum of the three

angles at the vertices would be more than 180 degrees. Unlike the Euclidean case,

where it’s always 180 degrees. Question? AUDIENCE: Yeah. Is the 3D curving happening

in a fourth dimension? Just like these 2D models

assume another dimension? PROFESSOR: Good question. The question was,

is the 3D curvature happening in a fourth dimension

just like this 2D curvature is happening in a

third dimension? The answer I guess is yes. But I should maybe clarify

the “just like” part. The third dimension here from

a strictly mathematical point of view allows us to visualize

the sphere in an easy way, but the geometry of the

sphere from the point of view of people who study differential

geometry is a perfectly well defined two dimensional

space without any need for the third

dimension to be there. The third dimension is

really just a crutch for us to visualize it. But that same crutch does work

in going from three to four. And in fact when we study the

three dimensional curved space of the closed universe, we will

in fact do it exactly that way. We’ll introduce the same crutch,

imagine it in four dimensions, and it will be very closely

analogous to the two dimensional picture

that you’re looking at. OK. So one of the possibilities

is a closed geometry where the sum of the

three angles of a triangle is always bigger

than 180 degrees. Another possibility

is something that’s usually described

as saddle shaped, or a space of

negative curvature. And in that case the sum

of the three angles– they get pinched, and

the sum of the angles is less than 180 degrees. And only for the flat case is

the sum of the three angles exactly 180 degrees, which is

the case of Euclidean geometry. The geometries on the

surfaces of these objects is non-Euclidean,

even though if you think of the three dimensional

geometry of the objects embedded in three dimensional

space, that’s still Euclidean. But the restricted geometry to

the two dimensional surfaces are non-Euclidean there and

there, but Euclidean there. And that’s exactly the way it

works in general relativity. There are closed universes with

positive curvature and the sum of angles being more

than 180 degrees. And there are open universes

where the sum of three angles is always less than 180 degrees. And there’s the

flat case– which is just on the

borderline of those two– where Euclidean geometry works. And the point is

that in our universe, Euclidean geometry

does work very well. That’s why we all learned

it in high school. And in fact we have

very good evidence that the early universe

was rather extraordinarily close to this flat case

of Euclidean geometry. And that’s what we’re trying

to understand and explain. According to general relativity

this flatness of the geometry is determined by

the mass density. There’s a certain value

of the mass density called the critical density– which

depends on the expansion rate, by the way, it’s not a

universal constant of any kind. But for a given

expansion rate one can calculate a

critical density, and that critical

density is the density which makes the universe flat. And cosmologists define a number

called omega– capital omega– which is just the ratio

of the actual mass density to the

critical mass density. So omega equals 1 says

the actual density is the critical

density, which means the universe would be flat. Omega bigger than 1 would be

a closed universe, and omega less than 1 would

be an open universe. What’s peculiar about the

evolution of this omega quantity is that omega

equals 1 as the universe evolves in

conventional cosmology behaves very much like a

pencil balancing on its tip. It’s an unstable

equilibrium point. So in other words, if omega

was exactly equal to 1 in the early universe, it would

remain exactly equal to 1. Just like a pencil that’s

perfectly balanced on its tip would not know which way to

fall and would in principle stay there forever. At least with

classical mechanics. We won’t include quantum

mechanics for our pencil. Classical pencil that we’re

using for the analogy. But if the pencil leans just

a tiny bit in any direction, it will rapidly start to

fall over in that direction. And similarly if omega

in the early universe was just slightly

greater than 1, it would rapidly rise

towards infinity. And this is a closed universe. Infinity really means

the universe has reached its maximum size, and it

turns around and collapses. And if omega was

slightly less than 1, it would rapidly

dribble off to 0, and the universe would

just become empty as it rapidly expands. So the only way for omega

to be close to 1 today– and as far as we can

tell, omega is consistent with 1 today– the only

way that can happen is if omega started out

unbelievably close to 1. Unless it’s this pencil

that’s been standing there for 14 billion years and

hasn’t fallen over yet. Numerically, for omega to be

somewhere in the allowed range today, which is

very close to 1, it means that omega at one

second after the Big Bang had to be equal to 1 to the

incredible accuracy of 15 decimal places. Which makes the value

of the mass density of the universe at one second

after the Big Bang probably the most accurate number

that we know in physics. Since we really know it

to 15 decimal places. So if it wasn’t

in that range, it wouldn’t be in the

[? lab manuals ?] today. We have this

amplification effect of the evolution

of the universe. So the question is,

how did this happen? In conventional Big Bang theory,

the initial value of omega could have been

anything, logically. To be consistent with

what we now observe it has to be within this

incredibly narrow range, but there’s nothing

in the theory which causes it to be in

that narrow range. So the question

is, why did omega start out so

incredibly close to 1? Like the earlier problem

about homogeneity, if you want to just assume

that it started out– exactly like, it had to be– at omega

equals 1, you could do that. But if you want to have any

dynamical explanation for how it got to be that

way, there’s really nothing in conventional

cosmology which does it. But in fact, inflation does. In the inflationary model we’ve

changed the evolution of omega because we’ve turned gravity

into a repulsive force instead of an attractive force, and that

changes the way omega evolves. And it turns out that

during inflation, omega is not driven away

from 1– as it is during the entire rest of

the history of the universe– but rather during inflation

omega is driven rapidly towards 1, exponentially

fast, even. So with the amount

of inflation that we talked about– inflation by a

factor of 10 to the 28 or so– that’s enough so that the

value of omega before inflation is not very much constrained. Omega could have started out

before inflation not being 1, but being 2 or 10 or

1/10 or 100 or 1/100. The further away you

start omega from 1, the more inflation you need

to drive it to 1 sufficiently. But you don’t need

much more inflation to make it significantly

far away from 1 because of this fact the

inflation drives omega to 1 exponentially. Which really means it’s a

very powerful force driving omega to 1. And giving us a very

simple, therefore, explanation for why omega

in the early universe appears to have been

extraordinarily close to 1. So I think that’s– Oh, I

have a few more things to say. There’s actually a prediction

that comes out of this, because this tendency of

inflation to drive omega to 1 is so strong, that you

expect that omega really should be 1 today. Or to within

measurable accuracy. You could arrange

inflationary models where it’s say, 0.2–

which is what people used to think it was– but in order

to do that, you have to arrange for inflation to end

at just the right time before it makes it closer. Because every e-fold drives it

another factor of 10 closer. So it’s very rapid effect. So if you don’t fine tune

things very carefully, most any inflationary model will

drive omega so close to 1 that today we would see it as 1. That did not used to

appear to be the case. Before 1998 astronomers

were pretty sure that omega was only 0.2 or

0.3, while inflation seemed to have a pretty clear

prediction that omega should be 1. This personally I found rather

uncomfortable, because it meant whenever I had dinner

with astronomers, they would always sort

of snidely talk about how inflation was

a pretty theory, but it couldn’t be right

because omega was 0.2, and inflation was

predicting omega is 1. And it just didn’t fit. Things changed a lot in 1998,

and now the best number we have– which comes from the

Planck satellite combined with a few other

measurements, actually– is that now the observational

number for omega is 1.0010, plus or minus 0.0065. So the 0.0065 is

the important thing. This is very, very close

to 1, but the error bars are bigger than this difference. So it really means to about

a half a percent or maybe 1%, we know today that

omega is 1, which is what inflation would predict. That it should essentially

be exactly 1 today. The new ingredient that

made all this possible, that drove– changed

the measurement of omega from 0.2 to 1 is

a new ingredient to the energy budget of the

universe, the discovery of what we call dark energy. And we’ll be learning

a lot about dark energy during the course of the term. The real discovery in 1998

was that the universe is not slowing down under the

influence of gravity as had been expected until that

time, but rather the universe actually is accelerating. And this acceleration has to

be attributed to something. The stuff that it’s attributed

to is called the dark energy. And even though there’s

considerable ignorance of what exactly

this dark energy is, we can still calculate

how much of it there’s got to be in order to

produce the acceleration that’s seen. And when all that

is put together, you get this number, which is

so much nicer for inflation than the previous number. Yes. AUDIENCE: So, was the

accelerating universe like the missing factor which

they– gave a wrong assumption which made them think

that omega was 0.2 or 0.3? PROFESSOR: Yeah, that’s right. It was entirely

because they did not know about the

acceleration at that time. They in fact were accurately

measuring the stuff that they were looking at. And that does only

add up to 0.2 or 0.3. And this new ingredient,

the dark energy, which we only know about

through the acceleration, is what makes the difference. Yes. AUDIENCE: And that data

that they were measuring is really just sort of

the integrated stuff in the universe that we

see through telescopes? Very straight-forward

in that way? PROFESSOR: That’s right. Including dark matter. So it’s not everything

that we actually see. There’s also– not

going into it here, but we will later in the

course– there is also stuff called dark matter, which is

different from dark energy. Even though matter and energy

are supposed to be the same, they are different

in this context. And dark matter is

matter that we infer exists due to its

effect on other matter. So by looking, for example,

at how fast galaxies rotate, you can figure out

how much matter there must be inside

those galaxies to allow those

orbits to be stable. And that’s significantly more

matter than we actually see. And that unseen matter is

called the dark matter, and that was added

into the 0.2 or 0.3. The visible matter

is only about 0.04. OK. So, so much for the

flatness problem. Next item I want talk about is

the small scale nonuniformity of the universe. On the largest

scale, the universe is incredibly uniform– one

part in 100,000– but on smaller scales, the universe

today is incredibly lumpy. The earth is a big lump

in the mass density distribution of the universe. The earth is in fact

about 10 to the 30 times denser than the average matter

density in the universe. It’s an unbelievably

significant lump. And the question is, how

did these lumps form? Where did they come from? We are confident that

these lumps evolved from the very

minor perturbations that we see in the

early universe, that we see most clearly

through the cosmic background radiation. The early universe we believe

was uniform in its mass density to about one part in 100,000. But at the level of

one part in 100,000, we actually see in the

cosmic background radiation that there are nonuniformities. And things like the

Earth form because these small nonuniformities

in the mass density are gravitationally unstable. In regions where there’s

a slight excess of matter, that excess of matter

produces a gravitational field pulling more matter

into those regions, producing a still stronger

gravitational field pulling in more matter. And the system is unstable,

and it forms complicated lumps which are galaxies,

stars, planets, et cetera. And that’s a complicated story. But it all starts from these

very faint nonuniformities that existed, we believe,

shortly after the Big Bang. And we see these nonuniformities

in the cosmic background radiation, and

measuring them tells us a lot about the

conditions of the universe then, and allows us

to build theories of how the universe

got to be that way. And that’s what these satellites

like COBE, WMAP, and Planck are all about– measuring

these nonuniformities to rather

extraordinary accuracy. Inflation has an

answer to the riddle of where the

nonuniformities came from. In the conventional

Big Bang theory, there was really

just no explanation. People just assumed they were

there and put them in by hand, but there was no theory of

what might have created them. In the context of

inflationary models where all the matter really is

being created by the inflation, the nonuniformities are also

controlled by that inflation, and where nonuniformities

come from is quantum effects. It’s a little hard to believe

that quantum effects could be important for the large

scale structure of the universe. The Andromeda

galaxy doesn’t look like it’s something

that should be thought of as a

quantum fluctuation. But when one pursues this

theory quantitatively, it actually does work very well. The theory is that

the ripples that we see in the cosmic

background radiation really were purely the

consequence of quantum theory– basically the uncertainty

principle of quantum theory, which says that it’s just

impossible to have something that’s completely uniform. It’s not consistent with

the uncertainty principle. And when one puts in the basic

ideas of quantum mechanics, we can actually calculate

properties of these ripples. It turns out that we

would need to know more about the physics

of very high energy– the physics that was

relevant during the period of inflation– to

be able to predict the actual amplitude

of these ripples. So we cannot predict

the amplitude. In principle, inflation

would allow you to if you knew enough about the

underlying particle physics, but we don’t know that much. So in practice we cannot

predict the amplitude. But inflationary models

make a very clear prediction for the spectrum of

these fluctuations. And by that I mean how

the intensity varies with wavelength. So the spectrum really

means the same thing as it would mean for

sound, except you should think about wavelength

rather than frequency because these waves

don’t really oscillate. But they do have wavelengths

just like sound waves have wavelengths, and if you

talk about the intensity versus wavelengths,

this idea of a spectrum is really the same

as what you’ll be talking about with sound. And you can measure it. This is not quite the

latest measurements, but it’s the latest measurements

that I have graphed. The red line is the

theoretical prediction. The black dots are

the measurements. This goes through the

seven year WMAP data. We have a little

Eureka guy to tell you how happy I am about this curve. And I also have graphs of what

other ideas would predict. For a while, for example, people

took very seriously the idea that the randomness that

we see in the universe– these fluctuations–

may have been caused by the random

formation of things called cosmic strings

that would form in phase transitions

in the early universe. That was certainly a

viable idea in its day, but once this

curve got measured, the cosmic strings were

predicting something that looked like that, which is

nothing at all like that curve. And they have since

been therefore excluded as being the source of density

fluctuations in the universe. And various other

models are shown here. I don’t think I’ll take the time

to go into, because there are other things I

want to talk about. But anyway, marvelous success. This is actually

the latest data. This is the Planck data that

was released last March. I don’t have it plotted

on the same scale, but again you see

a theoretical curve based on inflation

and dots that show the data with little

tiny error bars. But absolutely gorgeous fit. Yes. AUDIENCE: What happened to

your theory of inflation after they discovered

dark energy? Did it change significantly? PROFESSOR: Did

the theory change? AUDIENCE: Or like,

in the last graph there was a different curve. PROFESSOR: Well it’s plotted

on a different scale, but this actually is pretty much

the same curve as that curve. Although you can’t tell. AUDIENCE: Sorry. PROFESSOR: Oh. Oh, inflation without

dark energy, for example. I think it’s not so much

that the theory of inflation changed between

these two curves, but the curve you

actually see today is the result of what things

looked like immediately after inflation combined with

the evolution that took place since then. And it’s really

the evolution that took place since then that

makes a big difference between this inflationary curve

and the other inflationary curve. So inflation did not have

to change very much at all. It really did not. But of course it

looks a lot better after dark energy was discovered

because the mass density came out right, and gradually we

also got more and more data about these fluctuations

which just fit beautifully with what inflation predicts. OK. I want to now launch into

the idea of the multiverse. And I guess I’ll try to go

through this quickly so that we can finish. We’re not going try to

understand all the details anyway, so I’ll talk

about fewer of them for the remaining 10

minutes of the class. But I’d like to say a little

bit about how inflation leads to the idea

of a multiverse. Of course we’ll come back to it

at the very end of the class, and it’s certainly an exciting,

I think, aspect of inflation. The repulsive gravity material

that drives the inflation is metastable, as we said. So it decays. And that means that if

you sit in one place and ask where

inflation is happening, and ask what’s the probability

that it’s still happening a little bit later,

that probability decreases exponentially–

drops by a factor of two every doubling, every half life. But at the same time, the volume

of any region that’s inflating is also growing exponentially,

growing due to the inflation. And in fact in any

reasonable inflationary model the growth rate is vastly

faster than the decay rate. So if you look at

the volume that’s inflating, if you

wait for a half life, indeed half of that

volume will no longer be inflating– by the

definition of a half life. But the half that remains

will be vastly larger than what you started with. That’s the catch. And that’s a very

peculiar situation because it doesn’t

seem to show any end. The volume that’s inflating

just gets bigger and bigger even while it’s decaying,

because the expansion is faster than the decay. And that’s what leads to this

phenomena of eternal inflation. The volume that is inflating

increases with time, even though the inflating

material is decaying. And that leads to what we

call eternal inflation. The word “eternal” is

being used slightly loosely because eternal

really means forever. This is forever into the

future, as far as we can tell, but it’s not forever

into the past. Inflation would still start

at some finite time here, but then once it starts,

it goes on forever. And whenever a piece of

this inflating region undergoes a transition

and becomes normal, that locally looks

like a Big Bang. And our Big Bang would be

one of these local events, and the universe formed by

any one of these local events where the inflating

region decays would be called a

pocket universe. Pocket just to suggest

that there are many of them in the overall scale

of this multiverse. They are in some sense

small, even though they’d be as big as the

universe that we live in. And our universe would be one

of these pocket universes. So instead of one

universe, inflation produces an infinite

number, which is what we call multiverse. I might just say the

word multiverse is also used in other contexts

and another theories, but inflation, I think, is

probably the most plausible way of getting a

multiverse, and it’s what most cosmologists

are talking about when they talk

about a multiverse. OK. Now how does dark

energy fit in here? It plays a very important

role in our understanding. To review, in 1998

several groups– two groups of astronomers

discovered independently that the universe

is now accelerating, and our understanding

is that the universe has been accelerating for about

the last five billion years out of the 14 billion year

history of the universe. There was a period where

it was decelerating until five billion years ago. An implication of this is

that inflation actually is happening today. This acceleration of

the universe that we see is very much like inflation,

and we really interpret it according to similar

kind of physics. We think it has to be

caused by some kind of a negative pressure,

just as inflation was caused by a

negative pressure. And this material that

apparently fills space and has negative pressure is

what we call dark energy. And dark energy is

really just by definition the stuff, whatever

it is, that’s causing this acceleration. If we ask, what is the

dark energy, really? I think everybody agrees there’s

a definite answer to that, which is something

like, who knows? But there’s also a most

plausible candidate, even though we don’t know. The most plausible candidate–

and other candidates are not that different,

really, but we’ll talk about the most plausible

candidate– which is simply that dark energy

is vacuum energy. The energy of nothingness. Now it may be surprising that

nothingness can have energy. But I’ll talk about that, and

it’s really not so surprising. I’ll come back to that question. But if dark energy is really

just the energy of the vacuum, that’s completely

consistent with everything we know about, what we can

measure, the expansion pattern of the universe. Yes. AUDIENCE: Why is it that only

in the last five billion years has the universe

started accelerating? PROFESSOR: To

start accelerating. Right. Right. OK. I’m now in a

position to say that. I wasn’t quite when I

made the first statement, but now that I’ve said there’s

probably vacuum energy, I can give you an answer. Which is that vacuum

energy, because it is just the energy of the vacuum,

does not change with time. And that’s the same as what

I told you about the energy density during inflation. It’s just a constant. At the same time,

ordinary matter thins out as the universe

expands, throwing off in density like one over

the cube of the volume. So what happened was

that the universe was dominated by ordinary

matter until about five billion years ago, which

produced attractive gravity and caused the universe to slow. But then about five

billion years ago the universe thinned out enough

so that the ordinary matter no longer dominated over

the vacuum energy, and then the vacuum energy started

causing repulsion. Vacuum energy was there all

along causing repulsion, but it was overwhelmed

by the attractive gravity of the ordinary matter until

about five billion years ago. Does that make sense? AUDIENCE: Yes. PROFESSOR: OK. Good. Any other questions? OK. So. The first thing I want

to talk about here is why can nothing

weigh something? Why can nothing have energy? And the answer is

that actually this is something the physicists

are pretty clear on these days. The quantum vacuum, unlike

the classical vacuum, is a very complicated state. It’s not really empty at all. It really is a complicated

jumble of vacuum fluctuations. We think there’s even a field

called the Higgs field, which you’ve probably

heard of, which has a nonzero value in

the vacuum on average. Things like the photon field,

the electromagnetic field, is constantly oscillating

in the vacuum because of the uncertainty

principle, basically, resulting in energy density

in those fluctuations. So there’s no reason

for the vacuum energy to be zero, as far

as we can tell. But that doesn’t mean that

we understand its value. The real problem from the point

of view of fundamental physics today is not understanding

why the vacuum might have a nonzero energy density. The problem is understanding

basically why it’s so small. And why is smallness a problem? If you look at quantum field

theory– which we’re not going to learn in any detail–

but quantum field theory says that, for example,

the electromagnetic field is constantly fluctuating. Guaranteed so by the

uncertainty principle. And these fluctuations

can have all wavelengths. And every wavelength contributes

to the energy density of the vacuum fluctuations. And there is no

shortest wavelength. There’s a longest

wavelength in any size box, but there’s no

shortest wavelength. So in fact, when you try

to calculate the energy density of the vacuum in

the quantum field theory, it diverges on the

short wavelength side. It becomes literally infinite

as far as the formal calculation is concerned because all

wavelengths contribute, and there is no

shortest wavelength. So what does this mean

about the real physics? We think it’s not necessarily a

problem with our understanding of quantum field theory. It really is, we think,

just a limitation of the range of validity

of those assumptions. They certainly– quantum theory

works extraordinarily well when it’s tested in

laboratory circumstances. So we think that at

very short wavelengths, something must happen to

cut off this infinity. And a good candidate for what

happens at short wavelengths to cut off the

infinity is the effects of quantum gravity, which

we don’t understand. So one way of estimating

the true energy density as predicted by

quantum field theory is to cut things off at the

Planck scale, the energy scale, length scale, associated

with quantum gravity– which is about 10 to the

minus 33 centimeters. And if you do that, you

can calculate the number for the energy density of

the electromagnetic field of the vacuum and

get a finite number. But it’s too large. And too large not by a

little bit, but by a lot. It’s too large by 120

orders of magnitude. So we are way off in terms of

understanding why the vacuum energy is what it is since our

naive estimates say it should be maybe 120 orders

of magnitude larger. Now I should add that there

is still a way out here. The energy that

we calculate here is one contribution to

the total vacuum energy. There are negative

contributions as well. If you calculate the

fluctuations of the electron field, that turns out to be

negative in its contribution to the energy. And it’s always possible

that these numbers cancel– or cancel almost exactly– but

we don’t know why they should. So basically there’s a big

question mark theoretically on what we would predict for the

energy density of the vacuum. Let’s see. What should I do here? I am not going to be able

to finish this lecture. I think it’s worth

finishing, however. So I think what I’ll do is I’ll

maybe go through this slide and then we’ll just stop, and

we’ll pick up again next time. There are just a few

more slides to show. But I think it’s an interesting

story worth finishing. But to come to a good

stopping place here– we still have a minute

and a half, I think. I want to say a little bit about

the landscape of string theory, which is going to be a possible

explanation– only possible, it’s very speculative here– but

one possible explanation which combines inflation, the eternal

inflation, and string theory produces a possible explanation

for this very small vacuum energy that we observe. It’s based on the idea

that string theory does not have the unique vacuum. For many years string

theorists sought to find the vacuum of string

theory with no success. They just couldn’t

figure out what the vacuum of string

theory would look like. And then a little more than 10

years ago many string theorists began to converge

around the idea that maybe they could not

find a vacuum because there is no unique vacuum

to string theory. Instead, what they now

claim is that there’s a colossal number– they

bandy around numbers like 10 to the 500th power– a colossal

number of metastable states, which are long lived,

any one of which could look like a vacuum

for a long period of time, even though ultimately it

might decay or tunnel into one of the other metastable states. So this is called the

landscape of string theory. This huge set of

vacuum like states, any one of which could be

the vacuum that fills a given pocket universe, for example. When one combines this with

the idea of eternal inflation, then one reaches the conclusion

that eternal inflation would very likely

populate all of these 10 to the 500 or more vacua. That is, different

pocket universes would have different kinds

of vacuum inside them, which would be determined randomly as

the pocket universes nucleate, as they break off from

this inflating backbone. And then we would

have a multiverse which would consist

of many, many– 10 to the 500 or more–

different kinds of vacua in different pocket universes. Under this assumption,

ultimately string theory would be the assumed

laws of physics that would govern everything. But if you were living in one

of these pocket universes, you actually see apparent laws

of physics that would look very different from other

pocket universe’s. The point is that the

physics that we actually see and measure is low energy

physics compared to the energy scales of the string theory. So what we are seeing are

just small fluctuations in the ultimate scheme of

things about the vacuum that we live in. So the very particle

spectrum that we see, the fact that we see

electrons and quarks, quarks that combine to form

protons and neutrons– could be peculiar to

our particular pocket. And in other pockets there could

be completely different kinds of particles, which

are just oscillations about different kinds of vacuum. So even though the

laws of physics would in principle be

the same everywhere– the laws of string

theory– in practice the observed laws of

physics would be very different from

one pocket to another. And in particular

since there are different vacua in

the different pockets, the vacuum energy

density would be different in different pockets. And that variability of

the vacuum energy density provides a possible answer to

why we see such a small vacuum energy. And we’ll talk more about

that next time on Tuesday. See you then.

In the beginning was WORD,

The WORD was written by the formula: T=0K

T=0K is a fabric of EXISTENCE of EVERYTHING

===

اللهم لك الحمد على هاذه النعم.

Beats listening to a pedophile guy dressed up in a skirt talking about how an invisible man in the sky who hates shrimp and homosexuals created the universe and flat earth 6,000 years ago. Or talking snake, talking donkey, talking burning bush, people living in a fish, people turning into pillars of salt, virgin birth, worldwide flood, walking on water, water turning into wine and other miscellaneous religious stupidity…!!!

I love learning these things. I have an insatiable appetite for learning these complex topics in physics. On the other hand, religious dogma bores the hell out of me. Science is way more interesting and exciting than superstition.

Can someone tell me if universe is expanding then actual density of universe must be decreasing… Means value of omega is decreasing isn't it

Alan Guth, eres una vara!

OK, why is there a dildo next to the laptop….

It is pretty evident that the Big Bang was a game of hide and seek played by a some individual Verses in our Multiverse. BB 4305 was like, you AINT gonna catch me this time, and it’s literally been looking for it’s final hiding spot ever since. Taking it to an eternal level. When BB 4305 realises that it’s gone too far for it’s other verse friends to find it, it will just go all mega black hole to meet back with its friends and start the game again. Right?

Except we have now observational evidence whatsoever! This is theoretical speculative fantasy for the moment. For instance ne of our french physicist Jean-Pierre Petit ask physicists, in a karl schwarzschild cosmological seminar, if they have had read Schwarzschild's original paper and if they knew he did a second one and nobody out of 100+ people actually read it…

UNIVERSE IS ETERNAL https://www.youtube.com/watch?v=KXKid9j3klU&feature=youtu.be

God spoke and 'bang', it happened.

T.O.E. = GOD.

https://creation.com/the-universe-is-nothingness-the-latest-cosmological-wild-guess

David Barton tells the truth about America's Christian Foundation

https://m.youtube.com/watch?v=O1Qgg-v3AZQ

I applaud your institution for remaining open to comments. Certain other institutions are afraid of criticism. Imagine a system of science without dissent.

Very seldom do I see a lecture that walks through exactly how the data developed the theories we’ve applied.

I think we need an instrument(International Organization) to control global climate in the perspect of Orbital Mechanics. (including small debris and lanched projectile). I think that there are many forest fires than before

Genius

https://www.youtube.com/watch?v=NMaNsmShaik&t=1227s

I AM FROM ODISHA,INDIA AND I FOUND A NEW THEORY ABOUT UNIVERSE IF YOU WANT TO KNOW AND BUY CONTECT ME 9861476568

“The universe burst into something from absolutely nothing—zero, nada. And as it got bigger, it became filled with even more stuff that came from absolutely nowhere. How is that possible? Ask Alan Guth. His theory of inflation helps explain everything.”

So proclaimed the front cover of Discover magazine, April 2002.

https://creation.com/five-atheist-miracles

Listening to this makes me feel like the most privileged fly on the wall since the invention of the printing press.

Almost had a Nobel before the results were corrected.