Inflation

1
Inflation Sean Carroll, Caltech SSI 2009

1. The state of the universe appears finely-tuned
2. Inflation can make things smooth and flat
3. Primordial perturbations via quantum fluctuations
4. But there are conceptual problems

Refs Liddle, astro-ph/9901124 Langlois,
hep-th/0405053 Baumann, hep-th/0907.5424
2
1. The state of the universe appears
finely-tuned. The early universe was extremely
smooth and flat, even though these are unstable
conditions.
future -- emtpy space (1 trillion years) dilute
and cold
today -- galaxy distribution (14 billion years)
lumpy and sparse
early -- microwave background (380,000 years)
smooth and dense
3
The Friedmann equation with matter, radiation,
curvature
Matter and radiation dilute relative to
curvature as the universe expands. Curvature is
sub-dominant now, so must have been very small at
early times the Flatness Problem.
4
Our universe is also smooth 10-5 differences
in density between regions that were never in
causal contact. How did they know to agree?
The Horizon Problem.
5

• The flatness and horizon problem reflect the
  instability of the early universe deviations
  from perfect flatness or smoothness tend
  to grow with time.
• There are also problems with unwanted relics,
  such as magnetic monopoles. Of course, the
  nature and severity of such problems is
  highly model-dependent.

6
2. Inflation can make things smooth and flat.
Idea a tiny patch of the early universe is
dominated by persistent energy,forcing that patch
to expand exponentially, flattening and smoothing
along the way.
Alan Guth, in his office at SLAC, Dec 1979
SPECTATULAR REALIZATION This kind of
supercooling can explain why the universe today
is so incredibly flat.
7
Curvature dilutes away relative to inflationary
energy, which later converts into
matter/radiation (reheating).
density
inflation
radiation
radiation
curvature
time
8
Horizon problem is solved by stretching an
intially very tiny patch of space by a huge
factor (gt e60).
9
How does it work? Need an inflaton scalar field
with a very smooth potential, down which the
field slowly rolls.
V????
A potential works for inflation when
the slow-roll parameters are much less than unity.
??
10
What is the inflaton? No one knows.

• Higgs field from grand unification.
• Pseudo-Goldstone boson.
• Free scalar (m2?2) with m lt 10-6 MP .
• Supersymmetric moduli.
• D-brane coordinates in warped compactification.

11
3. Primordial perturbations via quantum
fluctuations.
Inflation tries to smooth out the universe, but
the uncertainty principle gets in the
way. Zero-point fluctuations in the inflaton
give rise to adiabatic density perturbations with
an approximately scale-invariant spectrum.
(flatter potential -gt more perturbations)
12
The amplitude of perturbations in the real
world is about 10-5. That depends directly on
the energy density during inflation, and weakly
on the slope of the potential. Plugging in
numbers Numerous assumptions ordinary
gravity, 4 dimensions, one scalar field, etc.
But at face value, it implies that inflation
happens near the Planck scale.
13
Acoustic peaks in CMB indicate that
perturbations are coherent -- they oscillate in
phase. That implies that perturbations
are primordial, not generated on sub-Hubble
scales in real time. Thats exactly what
inflation does -- not what you would get from
cosmic strings, etc.
WMAP
14
Inflationary perturbations are almost
scale-invariant, so we write the primordial
spectrum as Spectral index related to
slow-roll parameters Observations point to
0.9 lt nS lt 1.0
Tegmark
15
The inflaton isnt the only massless field lying
around theres also the graviton. So inflation
produces a spectrum of gravitational waves -gt
tensor perturbations.
Gravity waves induce B-mode (curl)
polarization in the CMB scalars induce E-mode
(gradient) polarization (detected).
16

• Good news
• Tensor amplitude directly probes energy scale
  of inflation
• Consistency relation in single-field models
  provides a test of inflation (V,
  ??????????AS,?AT,?nS,?nT)
• Bad news
• Amplitude can easily be low
• Consistency relation can easily be violated
• Large tensor/scalar ratio requires ?? gtgt MP
  hard to achieve in string theory

17
Spinoff quantum fluctuations can sometimes
push the inflaton field up the potential. Result
Eternal inflation, in which inflation continues
forever in some regions while ending in others.
V????
??
If string theory provides a landscape of
possible universes, eternal inflation can make
them all real.
Linde et al.
18
4. But there are conceptual problems.
Another way of thinking about the
fine-tuning problems targeted by inflation is in
terms of the entropy of the observable universe.
Our comoving patch isnt really a closed
system but its actually very close. Early and
late times are two different configurations
of the same system.
19
We dont have a general formula for entropy,
but we do understand some special cases. Thermal
gas(early universe) Black holes (today) d
e Sitter space (future universe)
20
Entropy goes up as the universe expands --
the 2nd law works! Consider our comoving patch.
time
early universe S Sthermal 1088
today S SBH 10100
future S SdS 10120
The fine-tuning of the early universe reflects
the fact that the entropy was low.
21
Does inflation explain that? Well, no. We tell
the following story. The early universe was a
chaotic, randomly-fluctuating place. But
eventually some tiny patch of space came to be
dominated by the potential energy of some scalar
field. That led to a period of accelerated
expansion that smoothed out any perturbations,
eventually reheating into the observed Big Bang.
The claim is finding such a
potential-dominated patch cant be that hard, so
our universe is (supposedly) natural.
today
time
inflationary patch
roiling high- energy chaos
22
But a randomly fluctuating system is most
likely to be in a high-entropy configuration.
And the entropy of the proto-inflationary patch
is extremely low!
Penrose
inflation S 1010 - 1015
today S SBH 10100
future S SdS 10120
CMB, BBN S Sthermal 1088
The universe is less likely to inflate than just
to look like what we see today. Inflation makes
the problem worse.
23
Entropy measures volumes in phase space.
phase space
Boltzmann entropy increases because there are
more high- entropy states than low-entropy ones.
sets of macroscopically indistinguishable
microstates
24
Local, unitary dynamics can never, in principle,
explain why a system was naturally in a state
of low entropy -- that depends on how state
space is coarse-grained, not on the particular
choice of Hamiltonian.
Liouvilles theorem volume in phase space is
conserved under Hamiltonian evolution.
no no no!
There is no clever choice of dynamics which
naturally makes the early universe small, dense,
and smooth.
25
Inflation has a lot going for it it creates a
hot Big Bang cosmology out of a very simple
state, starting with a tiny patch of
potential energy. But why were the degrees of
freedom of our universe all squeezed
delicately into that patch in the first
place? Inflation might play a crucial role in
the real history of the universe. But it
doesnt relieve us of the ultimate
responsibility of finding a real theory of
initial conditions.