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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
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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
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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.
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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.
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• 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.
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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.
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Curvature dilutes away relative to inflationary energy,which later converts into matter/radiation (“reheating”).
“density”
time
radiation
curvature
radiation
inflation
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Horizon problem is solved by stretching an intiallyvery tiny patch of space by a huge factor (> e60).
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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.
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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.
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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)
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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.
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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]
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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]
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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).
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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
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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.]
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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.
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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)
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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.
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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
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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]
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phasespace
sets of macroscopicallyindistinguishable microstates
Entropy measures volumes in phase space.
Boltzmann: entropyincreases becausethere are more high-entropy states thanlow-entropy ones.
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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!
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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.