1. Inflationary Cosmology: Is Our Universe Part of a Multiverse? Part I

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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


  • 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

  • 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…

  • God spoke and 'bang', it happened.
    T.O.E. = GOD.

    David Barton tells the truth about America's Christian Foundation

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

  • 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

  • “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.

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