InflationSean Carroll, Caltech

SSI 2009

1.The state of the universe appears finely-tuned2.Inflation can make things smooth and flat3.Primordial perturbations via quantum fluctuations4.But there are conceptual problems

Refs: Liddle, astro-ph/9901124; Langlois, hep-th/0405053; Baumann, hep-th/0907.5424

early -- microwave background(380,000 years): smooth and dense

today -- galaxy distribution(14 billion years): lumpy and sparse

1. The state of the universe appears finely-tuned.

The early universe was extremely smooth andflat, even though these are unstable conditions.

future -- emtpy space(1 trillion years): dilute and cold

The Friedmann equation with matter, radiation, curvature:

Matter and radiationdilute relative to curvatureas the universe expands.Curvature is sub-dominantnow, so must have beenvery small at early times:

the Flatness Problem.

Our universe is also smooth: 10-5 differences in density between regions that were never in causal contact.

How did they know to agree?

TheHorizonProblem.

• 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.

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.

2. Inflation can make things smooth and flat.

Idea: a tiny patch of the early universe is dominatedby persistent energy,forcing that patch to expandexponentially, flattening and smoothing along the way.

Curvature dilutes away relative to inflationary energy,which later converts into matter/radiation (“reheating”).

“density”

time

radiation

curvature

radiation

inflation

Horizon problem is solved by stretching an intiallyvery tiny patch of space by a huge factor (> e60).

How does it work? Need an inflaton scalar field witha very smooth potential, down which the fieldslowly rolls.

V

A potential works forinflation when theslow-roll parametersare much less than unity.

What is the inflaton? No one knows.

• Higgs field from grand unification.

• Pseudo-Goldstone boson.

• Free scalar (m22) with m < 10-6 MP .

• Supersymmetric moduli.

• D-brane coordinates in warped compactification.

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 riseto adiabatic density perturbations with anapproximately scale-invariant spectrum.

(flatter potential -> more perturbations)

The amplitude of perturbations in the real worldis about 10-5. That depends directly on the energydensity during inflation, and weakly on the slopeof the potential. Plugging in numbers:

Numerous assumptions: ordinary gravity, 4 dimensions,one scalar field, etc. But at face value, it impliesthat inflation happens near the Planck scale.

Acoustic peaks in CMB indicate that perturbationsare coherent -- they oscillate in phase.

That implies that perturbations are primordial, not generated on sub-Hubble scales in real time.

That’s exactly what inflation does -- not whatyou would get from cosmic strings, etc.

[WMAP]

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 < nS < 1.0

[Tegmark]

The inflaton isn’t the only massless field lying around:there’s also the graviton. So inflation produces aspectrum of gravitational waves -> tensor perturbations.

Gravity waves induceB-mode (curl) polarizationin the CMB; scalarsinduce E-mode (gradient)polarization (detected).

Good news:

• Tensor amplitude directly probesenergy 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 >> MP; hardto achieve in string theory

V

Spinoff: quantum fluctuations can sometimes pushthe inflaton field up the potential. Result:

Eternal inflation, in which inflationcontinues forever in some regions while ending in others.

If string theory provides alandscape of possibleuniverses, eternal inflationcan make them all real.

[Linde et al.]

4. But there are conceptual problems.

Another way of thinking about the fine-tuningproblems targeted by inflation is in terms of theentropy of the observable universe.

Our comoving patch isn’t really a closed system; but it’s actuallyvery close. Earlyand late times aretwo differentconfigurations ofthe same system.

We don’t have a general formula for entropy, butwe do understand some special cases.

Thermal gas(early universe):

Black holes(today):

de Sitter space:(future universe)

Entropy goes up as the universe expands -- the2nd law works! Consider our comoving patch.

early universeS ~ Sthermal ~ 1088

todayS ~ SBH ~ 10100

futureS ~ SdS ~ 10120

time

The fine-tuning of the early universe reflects the fact that the entropy was low.

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 bythe 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 can’t be that hard, so our universe is (supposedly) natural.

time

roiling high-energy chaos

today

inflationarypatch

But a “randomly fluctuating” system is most likelyto be in a high-entropy configuration. And the entropyof the proto-inflationary patch is extremely low!

CMB, BBNS ~ Sthermal ~ 1088

todayS ~ SBH ~ 10100

futureS ~ SdS ~ 10120

The universe is less likely to inflate than just to look likewhat we see today. Inflation makes the problem worse.

inflationS ~ 1010 - 1015

[Penrose]

phasespace

sets of macroscopicallyindistinguishable microstates

Entropy measures volumes in phase space.

Boltzmann: entropyincreases becausethere are more high-entropy states thanlow-entropy ones.

Local, unitary dynamics can never, in principle, explainwhy 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.

There is no clever choice of dynamics which naturallymakes the early universe small, dense, and smooth.

Liouville’s theorem:volume in phase spaceis conserved underHamiltonian evolution.

phasespace

no no no!

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 doesn’t relieve us of the ultimate responsibility of finding a real theory of initial conditions.