Cosmic Inflation

Ned
Wright's Cosmology Tutorial

Cosmos in a
Computer

Wayne Hu's Web Page

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 7o to
90o

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

How can the temperature be the same at an angle of
60o 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 60o 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 2o 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 60o 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 Msun

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: