So, we have our model. It's called Lambda Cold Dark Matter
Cosmology because it assumes that the missing energy in the universe beyond the
5% that is us, is dark matter, which is cold because we want it to clump to form
the dark matter outline of galaxies. We said that we are not talking about
relativistic particles, but about particles that are very massive when we
talked talked about dark matter and lambda for cosmological constant and this
is LCDM standard cosmology. And the problem is solved, right? Not
everything. So, there are some issues in the study of
cosmology and in another one of the fun parts of this field the study of the
universe at its very largest reduces the study of the universe at very small sizes
because you need to study what is very far, what is very far you're seeing into
the deep past. In the deep past, it was actually very
dense. Now I want to make a point about this
past and very dense. The universe in the past was very dense.
The universe is flat, we have every reason to assume that it is infinite.
one often hears that in the past, moments after the Big Bang, the entire universe
was a tiny, dense marble the size of a nucleus.
This is correct, but very misleading. Yes, the entire visible chunk of the
universe, the entire 46 million billion light years radius sphere that we see
today was, in fact, condensed to something the size of a nucleus at some
point. However, that was not the end of the
universe nor it, is there any reason to assume that that's the end of the
universe, anymore than there would have been a reason, 8 billion years ago for
some astronomer to conclude that the universe is only half that size.
Since then, our particle horizon has doubled and we see more of much the same
universe. And there's every reason to assume that
when see out to 62 billion light years, we will see about more of the same
universe. And what's more, this is also true of
someone who lives 40 billion light years that way and they see an additional 40
billion light years that way. So, we have every reason to assume that
the universe is homogeneous and isotropic even beyond what we've directly observed
because otherwise again, we're putting ourselves in some kind of crazy
anthropocentric. We're in the middle of the homogeneous
patch and there's an edge just beyond where we can see.
That's ridiculous. So, the universe was never the size of a
marble. The universe was very dense but if it's
infinite today, it was infinite then, it was just much denser.
Off the soap box. how does the physics of very small come
in? Well, of course, at early times and very high densities, by which time we
measure the density not by the redshift and not by the scale factor but by the
energy, effective energy KBT of the radiation dominated universe. So, when
this energy is above 10^19 GeV, a huge energy, this is in the first 5*10^-44
seconds after the Big Bang quantum gravitational effects are important.
So, this is the vicinity of the singularity.
Remember, that our expanding universe, if you follow it back, leads to an actual
singularity in the relativistic GR equations as actual singularity in the
sense that the curvature was infinite and everywhere in the distant past in this
infinite universe. at the Big Bang, curvature is infinite Gr
breaks down. A little bit after that, our
understanding of physics breaks down because so, maybe quantum gravity will
fix the singularity. even at energies below this Planck energy
of 10^19 GeV or times after 5810^-44. by the time you reach order, 10 orders of
magnitude higher, 10^-34 seconds KBT has dropped down to 10^15 GeV at that energy.
from that energy down, we sort of have a model of physics that works, the standard
model determines the physics. We have not made measurements up to that
energy, we have we have made measurements up to a 1,000 GeV but we think that we
have reason to understand that he next corrections to Physics are suggested at a
scale of about 10 to the 15 GeV. Above 10^15 GeV, we think We we have
reason, theoretical biases to suggest that, in fact, the electroweak and the
strong interaction are part of one grand unified theory.
There are various versions of the Grand Unified Theory, they share some common
properties but they would be necessary if you wanted to describe that part of the
history of the universe prior to 10^-34 seconds, and after, quantum gravity
corrections became unimportant. one aspect of this, is that if you tried
to make a prediction for the value of the cosmological constant, of the vacuum
energy, from these theories, well, you can build theories in which the
cosmological constant is 0 if, but if you don't build theories in which it's
exactly 0, then the typical value for lambda that you find is off by about
10^60. This is one of the largest glaring
misunderstood ununderstood aspects of physics.
so this is one problem to which I will not propose a solution today.
how to make a cosmological constant that is not zero and is not ridiculously
large. Open problem in particle physics and
again, with cosmological applications but it's in the nature of Physics at very
small scales to determine this. what are the problems beyond at energies
lower than that? Well, there are three famous problems with our scenario.
One is that the cosmic microwave background is so isotropic.
Well, I thought that was a great thing. It showed us that the universe is really
isotropic, yes, but how did it get so isotropic? So we computed that 1 degree
was the distance a sound wave could have traveled in the 380 degrees thousand
years since the Big Bang. light travels at a square root of 3
faster, so square root of 3 degrees is the size of a region in the sky that
light could have traveled since the Big Bang.
So, regions in the sky separated by more than the square root of 3 degrees had not
heard from each other by the time of recombination and by the this, the time
that the cosmic microwave background radiation that we see was emitted as
photons at 3,000 Kelvin. So, how could the temperature be so
precisely equal to within 1 part of 10^-5 in regions that had not talked to each
other? You'd expect fluctuations to cause one region to be hotter and another to be
colder and then heat to flow from the hot region to the cold region until
equilibrium. Yeah, but you can't establish equilibrium
if you haven't heard from each other yet. So, the very uniformity of the cosmic
microwave background is a puzzle, we have no mechanism. I mean, you can posit
initial conditions that very precisely homogeneous but that's unnatural, one
problem. Second problem is the flatness problem.
We measure that today's density is very close to the critical density, the
universe is almost exactly flat. Well, this tells you that in prior
epochs, the universe was even more flat. in particular, in our dust universe
where, remember, universe so, ignore the cosmological constant just so we can do
calculations. Imagine that we have a critical universe
where the only type of matter is dust, in other words rho of t is rho 0 times
a(t)^-3, that's what being dust buys me. And so, we have this relation that's it
well, it defined domain omega as 8 pi G rho over 3H^2.
So, at any time, H^2 omega is 8 opi G rho over 3 and in particular, this holds at
the present time with omega 0 and H 0. The other relation was that omega-1 was
this over H^2, a^2. So, I put the H^2 over here so H^2 times
omega-1 is kR0c^2/a^2. And now this is true at all times, so in
particular, I can write that H^2 omega at any time is the same as 8 pi G rho of t,
and this is related to H0^2 omegas 0 squared by the factor of a^-3.
And likewise, I can write that H^2 times omega-1 is H0^2 times omega0-1 except
times a^-2. So, I have here two equations, if I know
H0 and omega 0, I can figure H and omega. It's a little bit of Algebra, it's not
too bad, and what you find for omega is this beautiful equation over here,
omega-1, at any prior time, at any time in the evolution of a dust universe is
related to omega0-1, by this expression. But, so what does that tell me? That
tells me that if you go back to very small a in the dim past, then this term
is essential small. This is omega 0, and you find that
omega-1 is about a over omega 0, omega0-1.
So omega-1 is much smaller than omega0-1 in the limit when a becomes very small.
So, if we measure today, omega 0 approximately one to, within some
accuracy, say, 1 part in 100 then at early times, when a was 10^-18, omega-1
had to be 10^-18 more precisely 1. So again, posit initial conditions where
omega, if omega is ever exactly 1, then, of course, it stays 1.
So, one possibility is to find a mechanism that makes omega exactly 1.
Or posit initial conditions that omega was close to 1 to within 180 orders of
magnitude, or find a mechanism that makes that natural.
So, these are aesthetic problems. there's a third problem associated to
these GUT extensions of the standard model, they predict that as the universe
cools from the GUT scale of 10^15 GeV and below there will be relics left over,
magnetic monopoles that are stable and cannot decay unless they annihilate with
magnetic anti-monopoles, and for, depending on the extension, various other
relic particles. And magnetic monopole should be
detectable, there have been ongoing searches and we find none, you could
predict the density and we should have seen them by now.
So, where are the magnetic monopoles? these three problems were addressed by
something we'll talk about in the next clip.
there is the first problem of the vanishing of the cosmological constant or
the smallest of the cosmological constant is being addressed by theories of quantum
gravity about which we'll say little. there is fifth problem that
matter-antimatter asymmetry, the laws of Physics are almost but not quite
symmetric under the exchange of particles with antiparticles.
If they were precisely symmetric, then you would predict that the thermo bath
the hot, dense, earlier universe would produce, in equilibrium, as many
particles as antiparticles, as many antiprotons as protons, as many
antineutrons as neutrons, and so on. In fact, you might get a small imbalance
but it's important that you get an imbalance, because if you produced equal
numbers of muons and antimuons, then when they became non-relativistic, all the
muons would annihilate with all the antimuons and you'd have nothing left.
The reason we have something left is because, for some reason, more muons were
produced than antimuons. Now, this could be a fluctuation but then
you'd expect that if, that, that, by and large, maybe you'd have some regions of
the universe that are made of matter where matter predominates other regions
where antimatter predominates. But it's not true.
cosmic rays that arrive from large distance [UNKNOWN] in the universe show
us that our universe is almost exclusively made, all the galaxies and
the stars are almost exclusively made of protons.
There is not a star out there made up of antiprotons although in principle such a
thing could exist. Antiprotons could bind antielectrons and
produce atoms where everything is backwards,
but that does not happen. In our universe, there is this large
asymmetry. all the antimatter annihilated early and
what we're left with is a universe with protons and electrons and neutrons and no
antiparticles. this is a problem that's been studied a
lot. The conditions under which this asymmetry
could be formed using the known laws of Physics were formulated by Andrei
Sakharov in 1967. the problem is called the problem of
baryogenesis. There are many different models.
The, I think the currently favored one is associated with baryogenesis via
electogenesis. You generate an asymmetry in the lepton
sector, which leaks into an asymmetry in the production of protons and neutrons.
But this is an area of ongoing study, so there problems in cosmology that are not
yet solved. That's fine.
Something for you all to solve.