Cosmic Inflation

Outline

Big Bang Problems
The Inflationary Solution - Repulsive Gravity
Tests of Inflation?

Conceptual Problems with the Big Bang Theory

The Universe seems to have a number of special features that are not explained in the Big Bang Theory

several numbers which the theory doesn't specify must be fixed to very special values
This is called "fine-tuning" because these parameters must be "fine-tuned"

The Flatness-Oldness Problem

The Universe is now known have a density that is within a factor of 10 of the critical density

i.e. 0.1< < 10

This seems unremarkable now, but recall that = 1 is an unstable equilibrium point in the evolution of the Universe.

If = 1, at t = 1 ns, then = 1 will hold for all times,
but if = 1 + 10^-10, at t = 1 ns, then it would have recollapsed long ago
if = 1 - 10^-10, at t = 1 ns, then < 10^-20 today contrary to observation.
our limit of 0.1< < 10 today requires that

1-10^-24 < < 1+10^-24 at t = 1 ns
This is considered "fine tuning"

A similar example of unstable equilibrium

stand a pencil on it's point
at first it stays almost motionless, but it soon begins to tip
once it tips gravity pulls it in the same direction and it soon falls
with very careful positioning, we can make the pencil stand up for a longer time
but it would be hard to make it stay up for a year!

Here's how the Universe's scale factor a(t) would have evolved with different densities at 1 ns:

Recall the connection between the spatial curvature of the Universe and :

= 1 means a flat Universe - the 3-dimensional space is flat.

The Horizon Problem

This COBE-DMR map is supposed to be a temperature map of the Universe at the surface of last scattering when the Universe was about 300,000 years old:

The temperature anisotropy is ~ 10^-5 on scales between 7^o to 90^o
the spectrum obeys the "black body" curve to very high accuracy

normally a "black body" spectrum is seen from an object in thermal equilibrium
equilibrium occurs when the system has time to interact with itself and settles down to a steady state

An angle of 60^o corresponds to a distance today of about 15 billion light years

How can the temperature be the same at an angle of 60^o when the surface of last scattering was at t = 300,000 years?

a complication: The Universe expanded by a factor of ~1300 since t = 300,000 years
So, while an angle of 60^o corresponds to 15 billion light years today, it was only 12 million light years at t = 300,000 years
locations on the surface of last scattering separated by more than 2^o could never have communicated
Due to the speed of light limitation, they were out of "causal contact"

Why was the Universe the same temperature across the whole sky at t = 300,000 yrs?

In the Big Bang Theory - it must have started that way
another "fine tuning problem"

The Monopole Problem

now considered less important because it is based on a theory that is wrong
Electricity and Magnetism are very similar

in electromagnetic waves they are the same
the only difference is that we have particles of + and - electric charge
but we don't have N and S magnetic charges

break a magnet, and you get two with N and S poles
if we did, they'd be called magnetic monopoles

In the 1970's the "Standard Model" of particle physics was developed

it successfully describes all that is known of particle physics

More complete theories of particle physics called Grand Unified Theories (GUTs) were developed

they were very similar to the "standard model"
they "unified" 3 of the 4 forces (not gravity)
they predicted magnetic monopoles with a mass of 10¹⁶ proton masses

GUT monopoles should have about the same abundance as protons

too much dark matter
to reach is present size and expansion rate with this many monopoles, the Universe would have to be about 6,000 years old!

Either GUTs were wrong, or a way to get rid of the monopoles was needed

Inflationary Universe Solution

originally proposed by Starobinski (in Russian) to solve the Horizon and Flatness-Oldness Problem

in 1977 or 1978
no one noticed

In late 1979, Guth proposed a GUT theory version to solve the monopole problem

also solved Horizon and Flatness-Oldness Problems
GUT version of Inflation Theory later shown not to work
GUTs later shown to be wrong by failure to observe proton decay
big success for Guth

was a struggling post-doc with bleak job prospects
suddenly many job offers - now a tenured Prof. and MIT

Also provides a mechanism for generating the primordial seed density perturbations

which grow into galaxies and large scale structure
and were seen by COBE-DMR

One difficulty is that particle physics theory
Assumes that the Universe became dominated by the "false vacuum"

inflationary phase had accelerating expansion

The inflationary period was temporary, but the Universe expanded by a huge amount: ~ 10³⁰ or more

Inflationary solution to the Horizon Problem:

Suppose you have an intergalactic pen pal living in one of the "Great Wall" galaxies at a distance of ~200 million light years
You can communicate with her via radio waves

it takes 200 million years for a message to arrive, but this is much less than the age of the Universe (~1.3% of the age of the Universe)
because the Universe is expanding, each message will take longer to arrive
this because she is moving away from us, so each message has to travel farther.
as long as the expansion is slowing down, her velocity will be decreasing with time
we know the messages will reach her because she won't be going faster than the speed of light

Now, suppose the expansion of the Universe is accelerating

her velocity away from us will be increasing
eventually, her velocity will be > c (the speed of light) and we'll have lost a pen pal.
Note that v > c is ok as long as we are considering two objects far away in space.

It's just that the space in between us and our pen pal is increasing too fast for light to be able to make the trip
It's not so different from communication from inside a black hole

Inflation solves the horizon problem

at early times, a small bit of space interacts with itself

i.e. it's in causal contact

Inflation starts, and soon, this bit of space can no longer communicate with itself
Inflation ends, and the expansion starts decelerating again

the regions of space in "causal contact" become larger again
we see regions of space separated by 60^o on the surface of last scattering and we think that they are coming into "causal contact" for the 1st time
but according to inflation, they were in contact long ago as well
pre-inflation interactions may have set the temperature to be the same

Inflationary Solution to the Flatness-Oldness Problem

with ordinary matter and attractive gravity, = 1 is an unstable equilibrium point
with "false vacuum" matter and repulsive gravity, = 1 is a stable equilibrium point

gravity causes to get closer and closer to 1

with a long enough period of inflation, will become so close to 1 that it won't be too far from 1 today

most likely, = 1 still holds to high accuracy today (if inflation is right)
a "prediction"

Graphically, the spatial curvature evolves like the following during inflation:

before next... next... last

Here are "after" and "before" pictures:

Inflationary solution to the Monopole Problem

the rapid expansion quickly dilutes the density of monopoles to give ~1 monopole in the observable Universe
But, the same thing happens to all other particles!

observationally, we know there's more than 1 proton in the Universe!!

So Inflation seems to remove all the matter in the Universe
We need to create all the observed matter when inflation ends

this can be done through "false vacuum" decay
Many inflation models (including Guth's original one) fail to end with the production of matter
but some seem to work ok
successful models look "funny" from a particle physics point of view

Free Lunch

In the Big Bang, the whole Universe was once a tiny spec with a mass of > 10³⁰ M_sun
with Inflation, the entire Universe was once a tiny spec with a mass of < 1 gram
Where did all that energy come from?

Gravity: inflation creates a large positive matter energy and a large negative gravitational energy
Total energy of the Universe can be = 0!

Inflationary Solution to the Primordial Seed Problem

Inflation generates density perturbations through quantum fluctuations:
particle-antiparticle pairs are spontaneously created and annihilated on very short time scales.

this is a fundamental consequence of Quantum Mechanics and Heisenberg's Uncertainty Principle
it applies to all types of particles and fields

Density perturbations are produced by quantum fluctuations

normally, these would be on very tiny scales
but inflation boosts them to very large scales.

Inflation predicts that the primordial density perturbations will be about the same on all length scales

as observed
but, this is predicted by other primordial density perturbation theories, too.

Observational Predictions of Inflation

If inflation occurred at t = 10^-34 sec, how do we know if it really happened?
= 1 is sort of a prediction

but it was predicted by other arguments previously
< 1 models are also possible

scale independent amplitude of primordial seed perturbations

same prediction by other structure formation theories

The best hope: The detailed angular scale dependence of the CMBR anisotropies:

Here are the current observational results:

But MAP and PLANK should do much better: