Ay 21 – Lecture 6: The Early Universe
Module 6.1 - The Early Universe Introduction
[slide 1] Let us now turn to the study of the early universe.
[slide 2] First let me review a few of the key ideas. Obviously as already you were made to
realize, as you turn clock backwards and go to a smaller universe, it was hotter and denser, in a
fairly predictable way, since we know how matter behaves under high densities and
temperatures. Although of course, some new interesting Physics can happen such as inflation.
At any given time particles in universe have certain temperature, meaning certain energy and that
means that particles of different duress mass energies will dominate at different times.
Essentially universe acts as the ultimate accelerator, reaching energies of particles that will
probably never be generated in the lab, and thus, providing a very interesting new window into
particle physics itself.
So as we go deeper in the past, the energies increase, and we get into regimes for different
interactions and different particles become more dominant than others.
However, the price of that is that the deeper we go, the higher the energy, the less we actually
know. We currently probe physics out to the energies of order of 100 teraelectron volts of rest
mass. And we do have a fairly reliable theories what goes on up to there or thereabouts, but
beyond that things to get to be increasingly more speculative.
And in any case, at some point this has to break down. Currently the best guess is that it breaks
down around the Planck time, which is more less a guess. We will discuss Planck units later, but
at any rate. 10 ^-43 seconds is certainly the boundary of what we can even guess.
[slide 3] Here is just a schematic outline what history of the universe might look like. There is a
very early period of inflationary expansion, which is by now I think, fairly well established but is
by no means proven. And then we go through the early universe, a hot soup of quarks and other
particles until the atoms form, there are combined, micro backgrounds released and that's where
the astronomy as we know it really begins.
[slide 4] So let's go quickly through thermal history of the universe. What are the key moments?
At some point quantum gravity has to be important and dominate the physics of the universe. We
do not know when that is, we do not have a quantum theory of gravity. And Planck time, 10^-43
seconds is about as good guess as any. The inflation, if it happened, happened when the universe
was around 10^-33 seconds old. And shortly thereafter, we believe there was a grand unification
or rather, splitting of the electroweak interaction from the strong interaction. They split from
gravity sometime earlier, probably prior to the inflation.
When the universe was around a microsecond old, baryogenesis happens. Quarks create things
like protons and neutrons, particles that we know about. Between about 1 millisecond after the
Big Bang and about 3 minutes is the time of the cosmic nucleosynthesis, where the light
elements stabilize like Deuterium, helium 3, helium 4, lithium. Little bit of beryllium, maybe
even some boron were formed and frozen. At that time, universe is still very much dominated by
radiation.
That changes around 100,000 years, age, after which, matter becomes the dominant component
of the dynamics of the universe and first structures begin to form. The seeds of the first structures
begin to form from the dark matter itself. And when the universe was 380,000 years old, and we
know this number fairly well thanks to the procedure in cosmology measurements from cosmic
microwave background. The gas becomes neutral. Electrons and protons recombine become
atoms of hydrogen and helium and universe continues to expand.
At that time there are no more sources of light. There are no stars in the galaxies. They, these
being to, we think that they begin to form when the universe is few hundred million years old
and that point they can re-ionize the neutral gas of the universe and that is pretty much
completed by about age of 1 gigayear and that's where right now the frontier of our observational
cosmology is.
[slide 5] Physicists love to plot time history of the universe on a log axis because that gives lot
more space at very short times in which they're interested, and all of the known astronomy
happens just over there in the corner at the end.
Well, here is one from Mike Turner, and it's a handy little chart because shows you the
temperature, meaning the energy of the particles, the density, as well as the time when it
happened, which few of the key moments noted, just as I outlined a moment ago.
[slide 6] In tabular format, here is a quick outline, again, of what are the key times and particles
that dominate or, or processes that dominate at that time.
[slide 7] Not to be to boring, but here is another one. All of them contain more or less the same
information. I'm offering all of you, all of them to you because you may find one or the other
more useful, or, more clear than the others.
[slide 8] Well, what is the empirical evidence for all this? The first and foremost is the Cosmic
Microwave Background. Our direct probe of the early hot dense universe. So that reaches to the
times when universe is a few hundred thousand years old. Or actually, it's a little in excess of
1000. And it's certainly based on a very well understood atomic physics.
Next comes the cosmic nucleosynthesis, and that's based on well understood nuclear physics.
The results of that are abundances of light elements that we can test observationally today. So,
both experiments, in theory, seem to be fairly reliable, pushing in towards the big bang, all the
way down to maybe, 1 millisecond.
Beyond that, things get to be increasingly more speculative. We think that the a-symmetry
between matter and anti-matter in the universe was set around the time when the universe was
about a micro second old. This is based on a reasonably reliable physics of the standard model of
particle physics. Nevertheless it's not necessarily firmly established, but and you, you can think
of the actual observation that there is a lot more matter than anti-matter in the universe as an
evidence of may have happened when the universe was a micro-second old.
Then we reach the inflationary era, when universe was 10^-32 seconds old. Inflation makes, very
testable predictions, and so far seems to be doing fairly well. A lot of people believe that
something like inflation must have happened, which would be really remarkable giving us some
insight into physics of the universe when it was only 10^-32 seconds old.
But the upshot is that cosmological observations, observations of the largest things we can think
of, can constrain particle physics, micro-physics, at the smallest scales, we can also think of.
[slide 9] Well, let's first talk about the cosmic microwave background. In some sense, its
existence is trivial prediction of big bang theory. If the universe was expanding from hot and
dense state, then there has to be a thermal radiation relic from it. Initially, universe is all plasma,
everything is completely ionized, there are no atoms. And when it gets cold enough for atoms to
form, this is where this thermal radiation gets released. So Alpher, Herman, Gamow and others
made a prediction in 1940s and actually estimated that the temperature of the cosmic microwave
background would be around 5 degrees Kelvin.
It was only 1960s that cosmologists began to try to detect this in a serious fashion. And there
were upper limits until the actual discovery by Penzias and Wilson.
[slide 10] However, there was an even earlier not quite discovery, as early as in 1941. And here
is how. There are molecules in space and their clouds such as cyanogen; cyanogen happens to
have some energy transitions that are highly sensitive to temperature, and probe the regime
around a few Kelvin.
So Walter Adams, obtained observations, and McKellar had a theory inferring from these
observations of these subtle little lines of cyanogen that that gas was in a thermal bath of couple
degrees Kelvin. They didn't make anything out of it at the time. You could think of other ways to
heat up molecular clouds, like with starlight. And that stayed forgotten, certainly Gamow didn't
know about it, until Fred Hoyle, of all people, a person who was against the Big Bang, dug up
this evidence and pointed it out that this could be in fact a Consequence of this thermal
background from the early years.
[slide 11] But then again, it was a little too indirect and subtle for most people to believe. It took
really direct discovery by Penzias and Wilson to make the solid case for the existence of cosmic
micro background. Clearly this was a real milestone of cosmology.
[slide 12] So as we know, the universe is filled with thermal radiation, temperature is 2.7 degrees
Kelvin today, and is essentially a perfect black body. We have looked for deviations from the
black body spectrum, and none were found. You could imagine such things happening, if some
energetic processes in the early universe dumped extra energy into it and changed things away
from the equilibrium thermal black body radiation but evidently, this did not happen.
So the good news is that physics is well understood. We know exactly how this went. The bad
news is there were no surprises. There was no new physics to be found.
[slide 13] The key discoveries there came from the COBE satellite, Cosmic Background
Explorer. COBE was launched to probe the cosmic microwave background in ways that would
not be reachable from the ground, at least, not at the time. And here are pictures of cosmic micro
sky. This is, the top one has the contrast knob turned up to 1,000. And you can see the dipole
radiation, which was already known due to the motion of the milky way relative to the cosmic
micro background. Subtracting that, and turning the contrast knob to 100,000, you see a motley
sky, and a big plane of galaxy with thermal emission from dust and synchrotron electrons and
what not. And subtracting that galactic emission leaves just motley sky of fluctuations that were
primordial in nature.
Cosmologists long looked for those, but this was the first time they were actually really seen.
And it was one of the reasons why John Mather and George Smoot got Nobel Prize for some of
these discoveries.
[slide 14] So let's estimate when, exactly, the recombination of primordial plasma into the atoms
happens. Hydrogen becomes ionized if it absorbs photons with energies of 13.6 electron volts or
more. And this is 3 * Boltzmann constant * the equivalent temperature of the gas. So that
immediately implies temperature of around 50,000 degree kelvin.
However, it turns out, since there are many more photons than there are protons or electrons by,
by a factor of billion, even a tail of high energy photon, photons from a cooler gas or cooler
temperature would suffice. And we can estimate that using the Boltzmann equation for
equilibrium shown here.
And it happens that given this over abundance of photons over protons and electrons the
temperature could be as low as 2500 degrees and already one can get recombination. Since the
observed temperature of the micro background is now about 2.7 degrees, this immediately tells
you that this happened around redshift of 1100.
[slide 15] Well, obviously it doesn't happen all at once. There is a transition period as shown
here. What, what is plotted here is the fraction of ionized hydrogen in the universe, which begins
at unity. It's all completely ionized. Then, slowly, the gas recombines, the electrons are bound
into the atoms, and the process ends by about redshift of about 1,100.
So when we look at the cosmic micro background, what we're looking at is a photosphere of the
hot, ionized universe, inside out. When we look at the star we see a photosphere of ionized gas
from the outside in. So this is the inverted version thereof.
[slide 16] You may recall when we talked about models dominated by matter versus radiation,
that because the density, and it's density of photons changes in a steeper way with expansion than
it does of the matter, that two components must dominate with different times. The energy
density of the radiation decreases as the fourth power of the expansion factor, or for the matter,
it's only the third power, simply the evolution of the volume.
And, so given today's densities of matter and microbayron radiation, which is well determined
through Stefan Boltzmann formula, we can find at what point did these two cross. And the
answer is around redshift of 5,000. So this was before the recombination, but well after cosmic
nucleosynthesis was complete.
[slide 17] Next, we will talk about cosmic nucleosynthesis.
Module 6.2 - The Big Bang Nucleosynthesis
[slide 1] The existence of the cosmic microwave background is one of the two great predictions
of the Big Bang cosmology. The other one is the nucleosynthesis of light elements.
[slide 2] In the earlier stages of the expansion of the universe, there will be an equilibrium
between electrons, positrons, protons, neutrons, and both species of neutrinos, and the reactions
would work both ways and that lasts until the temperature drops to about 10 billion degrees or
age of the universe about the second. And simply, because the neutrons are a little heavier, there
will be fewer of them in the mix, which is why there will be asymmetry between them and
protons.
[slide 3] So their mass inequality causes asymmetry because of the beta decay and beta decay
reactions that convert one into the other. It requires little less energy to turn neutron into a proton
than the other way round, and so, that is the more favorite reaction. So after the annihilation of
excess positrons, only neutrons can decay.
We can again compute the ratio of neutrons and protons using Boltzmann's formula, and indeed,
initially, at very high temperatures, there'd be slight asymmetry due to the reasons we just
described. But the asymmetry increases as the universe expands and it finally gets frozen at the
value of 0.227 when the universe is only 10^10 degrees hot.
[slide 4] So that's how many neutrons come out of the equilibrium, but then they start decaying
using in beta decay and have a mean lifetime of a little less than 15 minutes. So before they can
be combined with protons into helium or other like nuclei, the decay destroys about 25% of
them. By the time temperature drops to a billion degrees, neutrons and protons can combine to
form nuclei of helium according to these reactions. Some of those newly made nuclei of helium
are then dissociated by residual photons, but as the universe expands, they cool enough and so no
more association can occur.
So by the time the universe is little less than 15 minutes old and the temperature drops to 300
million Kelvin, all of these ratios are frozen and those are the abundances that we will observe.
[slide 5] Actually, the real network of reactions is a little more complicated and here it's shown.
However the story we just went through pretty much captures the essence of it, but people who
model cosmic nuclear synthesis have to actually do the full-blown reaction network.
[slide 6] And the models predict how the abundances of different nuclear species will change in
time as all this is going on as shown here. Now you can see that by the time it's all over, say 15
minutes after the Big Bang, the lines remain flat, except of course, for small residual number of
neutrons that keep decaying.
[slide 7] At this point, the neutron to proton ratio has dropped to 0.14 and these neutrons end up
in the light nuclei that are produced. This is roughly 25% by mass and this is why there's about
25% by mass of primordial helium.
So in this way, the intrinsic mass difference between protons and neutrons, something that comes
out of particle physics, determines the abundances of light nuclei created in the Big Bang.
Since, essentially all neutrons are tied up in helium, its abundance is not dependent on density,
but some of the other species, they do depend on the actual baryonic density. That the reason the
reactions don't proceed beyond lithium or beryllium or so, is the universe expands and becomes
insufficiently hot and dense to create heavier nuclei.
[slide 8] Obviously, the heavier nuclei have higher charges and there is a higher Coulomb barrier
to be overcome. So after helium, there is a big gap going to lithium, and then also another one
going to boron, which is what limits the abundance of those elements.
[slide 9] The Big Bang nucleosynthesis predicts abundances of light nuclei. And generally, this is
parameterized as the ratio of the number of baryons to photons, which is frozen after all this is
complete. Since there is roughly a billion photons for every baryon, usually 10^10 are units that
are used here, and this ratio is closely related to the baryonic density according to the following
simple formula.
Since this ratio is preserved after all this is complete, we can measure it today and find out what
it was in the early years, which leads to the prediction that Omega baryons will be of the order of
4% and that is in an excellent agreement with the completely different argument from microwave
background fluctuations.
[side 10] Here, the predictions of the Big Bang nucleosynthesis in plot it in one diagram. The
different bands correspond to abundances of different nuclei at the end as a function of the
baryon density. The steeper the line, the more it's sensitive to abundance of baryons. And you
can see the deuterium will work best as a means of estimating the baryonic density in the
universe. Helium-4 does not work at all because the line is essentially flat.
[slide 11] The first confirmation of this is through measurement of the helium abundance. Starforming galaxies are used for this purpose, and since stars synthesize helium as well as heavier
elements, that should be in proportion. So by measuring abundance of other elements, say
oxygen, and then correlating it with abundance of helium should be a line that goes through zero
if there was no primordial helium created. However, because there was, then the intercept on the
y-axis gives you the primordial abundance of helium. And that number is a little less than 24% is
in an excellent agreement with predictions of the Big Bang nucleosynthesis.
[slide 12] Remember that deuterium is the most sensitive one to the actual baryonic density. So,
measuring cosmic abundance of the deuterium before it's processed in stars gives us a means of
estimating the baryonic density of the universe.
The way this is done is through absorption lines in spectra of quasars. The hydrogen clouds are
called Lyman-alpha forest and there will be Lyman-alpha equivalent for deuterium line, because
of its topic shift, its wave length will be little shorter than hydrogen Lyman-alpha. So the idea is
to find clouds where there is enough of materials, so that the line is already, well saturated for
hydrogen, but not enough to cover the equivalent absorption from deuterium. And of the order of
dozens such systems have been measured, and from the relative abundance of the deuterium to
hydrogen in these clouds, we can infer the baryonic density.
[slide 13] Lithium is a little more complicated, because it's also generated in stars, and it's subject
to uncertainties of stellar structure and evolution. And so this is why it's not really used to
constrain nucleosynthesis. However, we note that its abundance is perfectly consistent with the
predictions that satisfy the other measurements like helium and deuterium.
[slide 14] And finally, all this also depends on the number of neutrino families, because that they
each have degree of freedom in the early universe, and the Big Bang nucleosynthesis predicts
that there should be only three of them, which is in agreement from what we know from particle
physics.
[slide 15] Next time, we'll talk about inflation.
Module 6.3 - The Cosmic Inflation
[slide 1] We now come to address Inflation, which is, de facto, the standard theory of Quantum
Cosmology today.
[slide 2] It really started in 1980, where Alan Guth physicist at MIT came up with what he
called a spectacular realization. This is a page from his journal at the time. Some of these ideas
have been already discussed by others but not known to Guth. And since then many other people
have improved the theory and added more to it.
[slide 3] Well, the reason why everybody got so excited and why inflation has achieved such a
great acceptance is that it solves three key cosmological problems which had no obvious solution
before.
The first one of those is so called flatness problem, why is the universe so close to being exactly
flat.
The second is the horizon problem, why was cosmic microwaves so uniform? We'll explain both
of these in a moment.
The third one is less obvious and this is, why there are no magnetic monopoles observable
today? Whereas many Big Bang theories predicted there should be copious amounts of them
created in the early universe.
Inflation also accounts for the observed power spectrum of galaxy clustering and those are
ostensibly fluctuations left over from an earlier phase of the universe.
It also predicts the existence of random cosmic gravitational wave background, but we're very
far from being able to detect such a thing, and implies that our universe is just a small part of a
much, much, much bigger universe.
[slide 4] Let's tackle the flatness problem first. In Friedmann Lemaitre models, omega always
evolves away from unity. So if the universe was slightly negative curvature, it'll become more so
as it evolves. If it was slightly positive curvature it'll become more so as it evolves.
A great demonstration of that is shown in this diagram due to Ned Wright. It shows the density
of the universe, one nanosecond after the big bang, and it was 400 something sextillion 16
grams per cubic centimeter. Add one more gram per cubic centimeter, universe becomes closed
and will collapse. Subtract one, and universe goes to expansion forever.
So this is extremely sensitive, even the slightest deviation of omega equal one from the early
universe would map into a much bigger deviation today. And yet we know the universe is very
close to flat, so we must have started really really close to flat, if not absolutely flat.
[slide 5] The horizon problem can be stated this way at any given time. you can receive signals
from points that are within the time elapse from the big bang. And the particle-horizon distance
is three times speed of the light times, the age of the universe at the time. Now remember that
early on scale factor goes as time to the 2/3 power, and so it means that the horizon expands
faster than the universe, and as time goes on you get to see more and more objects come into it.
Now look at cosmic microwave background. It originates from roughly redshift 1000, and so its
temperature back then was about 10^4.5 higher than it is today.
At that time the horizon distance was given by the formula that I just mentioned above, and since
then it's expanded by a factor of 1000. However, our horizon distance is bigger than that. And
therefore, there should be many disconnected, causally disconnected, regions in the sky, which
were not in a causal contact at the time with when microwave background was released.
So, even though we can see that there is one sky now, back then, patches of microwave
background sky that are more than say two degrees apart were not in a causal contact.
[slide 6] And yet, cosmic micro background is uniform to few parts in a million. So how did
these independent pieces of universe know to have the same temperature within a part in a
million? Universes with which they could not have had physical contact.
[slide 7] The monopole problem is somewhat generic to the particle physics, and prediction is
that copious numbers of those will be generated during the grand unified theory transition, the
face transition. Yet none have been found despite many intensive searches. Not only that, but
their masses are supposed to be so high that coupled with density, they would totally dominate
the dynamics of the universe.
[slide 8] A generic expectation is that future theory of everything that unifies gravity with other
interactions, all interactions were unified into one, around Planck time or there abouts, the
universe undergoes a phase transition. Then the universe undergoes a phase where gravity splits
from the outer forces, and things remain roughly the same on the logarithmic time axis by almost
10 more powers of 10 when there is another phase transition.
What is postulated here, is that physical vacuum was not in its actual ground state at the time.
But it was at higher state, just like in atoms there is a ground state and then electrons can go to
higher orbits, and have excited states. Also supposedly the universe, the physical vacuum itself,
could've been in such a higher state. Somehow, and mechanisms for this are very complex and
beyond the scope of this class. The vacuum undergoes a phase transition going to the actual
ground state, the true vac
And in that process, vast amounts of energy are released and that energy is used to drive
exponential expansion.
[slide 9] Here is one schematic way to show it. The potential energy of some scale or field Pi is
plotted against potentially itself. And if universe is a center of a high plateau zero this is a
metastable state. It will eventually roll down into the true vacuum, which is at some finite value
of Pi, and may even slosh around a little bit. So in this schematic, the universe rolls down the
scalar field potential. So the decay of the field reheats the universe from that excess energy and
all of the matter/energy content of the universe can be created in that process.
[slide 10] So the universe undergoes phase transition and releases this latent heat inflating
exponentially. This could be just one of the many many bubbles in a much larger universe that
expand and maybe collide which is process called reheating. However, this is something that has
never been observed yet.
[slide 11] Now the energy density of a physical vacuum can be described as a cosmological
constant. This is not the cosmological constant of today, but some much larger value from the
earlier universe. In that case the Friedmann equation is give fairly simply and has an obvious
solution, an exponential expansion.
It turns out that in these inflationary models, this exponential expansion phase goes for about 100
e folding times or 40 orders of magnitude in size. And since the deviation of the density
parameter from unity also goes from exponentially. That means, there was incredibly finely
tuned to be close to unity to begin with.
[slide 12] So here is a schematic expansion diagram, it's plotted as 1 plus redshift rather than 1
over the quantity, which would be the scale factor. So there is a rapid initial expansion, and then
universe enters into a traditional Friedmann Lemaitre phase.
[slide 13] So how does this solve the flatness problem? Well think about, this as follows. You
can start with the region on a sphere, or this is now a 2 dimensional equivalent of 4 dimensional
space time. If you inflate this sphere by a large amount, that region will appear spatially flat, and
by that same token this great expansion of the universe essentially flattens the local curvature
which might have been more substantial.
So the density parameter differs from unity by an epsilon, a very tiny number
[slide 14] At the same time to solves the horizon problem. Space can expand faster than the
speed of light, so the regions that were constantly disjoint at the time of the recombination might
have been spatially close to each other at the beginning of the inflation. They might be really
adjacent to each other and that's why they have same energy density or same temperature of the
microwave background today.
The inflation carries them apart, and so by the time, by the end of the inflation they were no
longer in a casual contact. But nevertheless, prior to that, they were nicely thermalized.
[slide 15] Inflation also tackled the origin of the large scale structure we see. In quantum physics,
the vacuum is not empty but it's populated by virtual particle-antiparticle pairs that appear and
disappear, subject to the uncertainty principle. They cause essentially quantum fluctuations of
energy density in the early universe.
Now inflation blows up these minute quantum fluctuations of physical vacuum to enormous size.
Where in fact, they can be really seeds of the large scale structure that we observed today. It is a
remarkable prediction, that time quantum fluctuations can result in larger structures that they're
observed.
And there is a specific prediction of the functional form of the power spectrum of these
fluctuations, which turns out corresponds fairly closely to what's observed. Note that this is not a
proof of inflation because one can come up with different ways to reach the same observed state
if large scale structure. But the consistency is certainly very encouraging.
[slide 16] Next time, we'll talk about even earlier universe.
Module 6.4 - The Very Early Universe
[slide 1] Let us now complete our inquiry into the early universe with even a little more
speculative things.
[slide 2] First something about general particular physics lore. The strengths of different
interactions change with energy. And one of the basic paradigms is that at sufficiently high
energies, different interactions become one. For example, the electromagnetic interaction and the
nuclear weak force become unified at energies corresponding to temperatures about 10 to 16
degrees. And that has been actually experimentally proven.
Similarly, it is believed that electroweak interaction and strong nuclear force will become unified
at energies of the order of 10^28 degrees Kelvin, which corresponds to about 10^-35 seconds
after the big bang.
And then, to extend this, and this is purely speculative, those interactions become unified with
gravity, at the Plank time, 10^-43 seconds.
[slide 3] Now, moving forward in time, the grand unified interaction, splits, and that corresponds
to phase transitions in the early universe, one of which could be driving the inflation.
[slide 4] So the temperatures of 10^28 degrees, there is electroweak interaction and a strong
nuclear force.
At temperatures at less than about 10^15 degrees electromagnetic and weak interactions split.
This is the part that's been actually probed by accelerators.
Deeper in the past we believed that electroweak interactions, strong nuclear force adjoined in
what's called the Grand Unified Theories which are actually are not entirely complete, but they're
reasonably strong theoretical background. And there are good reasons to believe that that's what
actually happens.
This is many orders of magnitude higher energies than what we can probe in terrestrial particle
accelerators so in some sense, the early universe is our only means of actually testing these
theories by seeing what they predict.
It is possible, but, by no means certain, that it was this particular phase transition that splits the
strong force from electroweak interaction that's responsible for driving the inflation.
[slide 5] Now, let's look at another important fact in the universe. And that is that, there is a lot
more matter than there is antimatter. Early on people thought that there could be a symmetry, but
there was simply no trace of substantial amounts of antimatter in the universe. We would have
seen much more in terms of annihilation radiation and so on.
Also, people who look for cosmic rays look hard to see what is the balance between Particles and
anti particles and all of the anti particles that have been seen so far, can be easily explained
through normal interactions.
So the universe is predominantly made out of matter, with antimatter being a negligible fraction
thereof. How did that come about?
[slide 6] This leads us into the topic of Cosmic Baryogenesis. The worded protons and neutrons
come from as opposed to the equal numbers of anti protons and anti neutrons. Theoretical ground
for this was actually laid by great Soviet physicist Andrei Sakharov as early 1967. He came up
with three conditions that need to be satisfied for this to work.
First, Baryon number, which we think is conserved, must be violated. And, we do not have any
experimental evidence for this. But it's not impossible. It has been predicted by a number of
more modern theories, it just hasn't been observed yet.
Second, there has to be charge and charge parity violation. For those of you familiar with basic
concepts in particle physics, you know what that means, that the reversals of charge or reversals
of charge and parity of spins can make Arrow of time, glide away. This has actually been
experimentally demonstrated as early as the 1960s.
And finally, there has to be some departure from thermal equilibrium. And the expansion of the
universe provides a natural way to do this. Since universe expands, the time is not homogeneous.
There is a difference between 1 direction of time and the other, and that's what provides the
necessary condition.
So nowadays most people believe that something like this was indeed responsible for
establishing the asymmetry between matter and anti-matter.
Note, in the early universe, that could have been vast amounts of antimatter. It just annihilated
and what's left, the small fraction that's left is regular matter.
[slide 7] Finally, let's talk about Planck Units. This is a system of units devised by Max Planck in
1899. Prior to relativity and prior to quantum theory. He asked a simple question. Meters and
seconds and such are simply human conventions, are there actually natural units, that he can
derive from, say universal constants, such as Newton's gravity constant, or speed of light, or
Planck's constant. And indeed, they are.
Shown here combinations of such fundamental physical constants that yield elementary units of
time, or length, or mass.
And so for the time it's 10^-43 seconds and this is called Planck time.
For space is about 10^-33 centimeters, that's called the Planck length.
And for mass, it's about 10^-5 grams, which is called the Planck mass.
Similarly, you can derive units for other physical quantities.
[slide 8] And then there are derived units. In any case, the advantage of Planck units is that,
indeed, they do not depend on any arbitrary conventions. They really are given by the constants
of nature. But that doesn't necessarily mean that they're somehow magical. We use them as
limiting units for quantum gravity say but we don't really know. And they may or may not be
entirely relevant.
Nevertheless, they're a useful set of units to consider when thinking about very early universe.
[slide 9] So as we approach the Planck era our knowledge breaks down. We do not yet have a
working quantum theory of gravity. Not for the lack of trying. Many smart theorists have been
working on this for a long time. And today we have String theory or M-theory or Branes and
things like that.
It's fair to say that none of those have yet produced a convincing unifying theory that will unify
quantum physics in gravity. Nevertheless there are prospects that that might happen.
There are also theoretical attempts to think what was this imply beyond the Big Bang. One of the
interesting theories is the so called Ekpyrotic cosmology, which essentially states that colliding
branes, which are essentially multi-dimensional super-duper particles, can dissipate enough
energy to create all of the mass energy in the universe.
There's also the concept of the String Landscape, saying that there about 10^500 different
universes, each of which could have different physical constants and different laws of nature.
Needless to say this is completely speculative at this point.
In either case the early universe certainly provides a high-energy physics laboratory at levels that
will never be achievable on this planet. And so the unification of high-energy physics, particle
physics and cosmology is likely to get even stronger.
[slide 10] Next, we will talk about the contents of the universe.