So, I like to describe some of the solutions people have come up with for
the 3 middle problems that we discussed. The horizon problem,
the flatness problem, and the relic problem.
And the collection of ideas that are developed to addressed this go under the
name of inflation. This was first publicly, in a well known
way developed by Allen Guth in 1980. Although there were Soviet efforts that
we did not hear about until later, and Guth's idea is the following. Imagine
that at early times, at 10 to the minus 36 seconds below the gut energy scale, so
after the grand unified theory time but before the electro weak transition, the
universe underwent exponential expansion by many orders of magnitude, 10 to the 30
say. Some large number, 10^50, so an
exponential expansion during which the scale factor grew by a factor of 10^50.
what does that mean? That means, remember an exponential expansion, once event
horizon continually shrinks, and so our particle horizon, what we can see After,
that expansion is the small fraction of it was then one particle horizon.
The entire observable universe was some tiny little fraction, of one region, that
was the pre-inflation of the pre-inflation horizon.
so that solves the horizon problem. You give things 10^-36 seconds to
equilibrate within the region of one horizon.
And then, you blow them up, so they, get pushed out, outside of the horizon.
And then, all the things that we are slowly seeing, moving into our particle
horizon, because our particle horizon growth are actually see things that we
have seen before, back in the first 10^-36 seconds, and so there is no news.
There's no surprise that the cosmic microwave background is so uniform.
It's so uniform precisely because we have inflated and all the things that are out
there are things that were causally connected with us prior to inflation.
Similarly, the exponential inflation drives omega to 1. You can see that from
the same equation that gave us the problem of fine tuning before. whatever
omega, remember that H squared omega minus 1 is always equal to this. in this
case an exponential expansion, the Hubble Constant is a constant, remember, and so
what that means is that as a grows by a factor of 10 to the 50 say, this
denominator gets bigger by a factor of 10 to the 100 and omega minus 1 has to
shrink by a factor of 10 to the 100. So whatever omega you started with, by
the end of inflation you have omega equals 1 and then you start the radiation
dominated area of our universe with omega equals 1 to a very high precision.
And therefore it's not surprising that we end up with omega equals 1 today.
And similarly, whatever density of relics you think that the gut transition has
produced is now decreased by [SOUND] spreading them out.
And if you have expansion by scale factor growing by 10 to the 50,
the relic density is diluted by 10 to the 150,
and you don't have a problem with the fact that we have not discovered
monopoles. So inflation is a great idea, and the question is, what does that mean?
So we understand the kinematics. We understand how to describe
exponentially expanding universes. We'll use that to describe our future,
but what does it mean, how do you have, ha-, what is the dynamics, what is the
how do you turn a cosmological constant on and then off?
Remember that we had sort of ideas in the context of quantum field theories for
generating cosmological constants, and they were indeed huge.
But how do you turn them on and off? Well in these quantum field theories and these
guts there are such things as sort of tunable vacuum energy densities
associated to expectation values of fields, sort of parameters, dynamical
degrees of freedom of these theories. The detail, a little bit beyond what we
need, you can find, and Gus's idea that the universe gets trapped in some false
vacuum. This has large energy density.
That triggers inflation and this lasts for a short time before the universe sort
of tunnels, decays out of this false vacuum to the true vacuum with lowered
energy. That energy difference is then released
that heats the universe. So the universe had been super-cooled in
some sense and then gets re-heated. The exit from the inflationary period
into, is, into the current era, into the true vacuum has all kinds of what's
called graceful exit problems. So a model was proposed called new
inflation, or slow roll inflation, in which this tunneling event from a
supercooled bubble-nucleation type phase transition like boiling water is replaced
by a very slow transition where the inflation era is a slow roll.
Where this parameter is rather than tunneling suddenly is very slowly
evolving, and then sinking into the true vacuum and
then subject to damped oscillations, which is how it re-heats the universe.
new inflation had it's own issues. an improved version or a modified version
with other features and problems called chaotic inflation, was proposed where the
phase transition is gone alltogether and quantum fluctuations play the role of
moving the field away from the actual vacuum whence it slowly rolls, and this
occurs locally. And the idea is that one of these quantum
fluctuation, fluctuations, in some region of The universe creates larger energy
density. This region then inflates very rapidly.
the fluctuation is then very rapidly thrown outside the particle horizon, and
therefore can no longer decay. It's sort of frozen in, and then a new
fluctuation occurs and that too is, blows up and is ejected from the horizon.
And so fluctuations are frozen in as they inflate, and this led to the idea that is
the sort of topical one called eternal inflation.
In eternal inflation, what one really imagines that you have a universe with a
large vacuum energy, so it's exponentially expanding and always has
been. And if it's infinite in that it expands
exponentially. small regions, of the universe, can
spontaneously decay to vacuum, of smaller vacuum energy.
So these regions are still exponentially expanding, but exponentially slower, than
the The the ambient, if you want universe,
are these baby universe. They pop off and from the point of view
of the large universe, since they're not expanding fast enough, their intersection
with the universe, with the, the universe they came from is exponentially shrinking
and on the other hand these regions are inflating, and so they undergo inflation
and can then re-heat and then produce the entire history of our universe.
And regions within them can further bubble off to even lower values of
lambda, and so you get this sort of a fleas on fleas picture of inflation.
And the result is many disconnected, causally disconnected patches.
This is the so-called multiverse. I have a feeling that I'm beginning to
talk about fantasies. Is any is this real, does any of this
mean anything for us, and the idea indeed is that exponential inflation can freeze
fluctuations. If we have some fluctuation and then
during the inflationary period, the wavelength of this grows beyond the
particular horizon, can no longer decay, just as it could not have formed at that
size. And what that means is that these frozen
fluctuations are the inhomogeneieties around which dark matter and then
subsequently barionic matter can collect so these are the seeds for structure
formation. We've not hand the time to discuss the
theory of structure formation. It's also a little bit technical,
but basically this makes predictions, these models make predictions about the
kind of distribution of clusters and galaxies that you might expect. And so,
in some sense, a model that predicts some kind of inflationary scenario, will also
make a prediction about the structure and the spectrum of perturbations, which will
lead to a prediction about inhomogeneities in our actual universe,
which you might actually compare with data.
So, in an indirect way, these causally disconnected multi-verse regions might
actually be, is part of some larger model, something you could verify.