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
- 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:
