Inflation Sean Carroll, Caltech SSI 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/ ; Langlois, hep-th/ ; Baumann, hep-th/

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 and flat, even though these are unstable conditions. future -- emtpy space (1 trillion years): dilute and cold

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.

Our universe is also smooth: differences in density between regions that were never in causal contact. How did they know to agree? The Horizon Problem.

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 dominated by persistent energy,forcing that patch to expand exponentially, 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 intially very tiny patch of space by a huge factor (> e 60 ).

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.

What is the inflaton? No one knows. Higgs field from grand unification. Pseudo-Goldstone boson. Free scalar ( m 2  2 ) with m < M P. 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 rise to adiabatic density perturbations with an approximately scale-invariant spectrum. (flatter potential -> more perturbations)

The amplitude of perturbations in the real world is about 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.

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. That’s exactly what inflation does -- not what you 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 < n S < 1.0 [Tegmark]

The inflaton isn’t the only massless field lying around: there’s also the graviton. So inflation produces a spectrum of gravitational waves -> tensor perturbations. Gravity waves induce B-mode (curl) polarization in the CMB; scalars induce E-mode (gradient) polarization (detected).

Good news: Tensor amplitude directly probes energy scale of inflation “Consistency relation” in single-field models provides a test of inflation ( V,  A S,  A T,  n S,  n T ) Bad news: Amplitude can easily be low Consistency relation can easily be violated Large tensor/scalar ratio requires  >> M P ; hard to achieve in string theory

 V  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. If string theory provides a landscape of possible universes, eternal inflation can make them all real. [Linde et al.]

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 isn’t really a closed system; but it’s actually very close. Early and late times are two different configurations of the same system.

We don’t have a general formula for entropy, but we do understand some special cases. Thermal gas (early universe): Black holes (today): de Sitter space: (future universe)

Entropy goes up as the universe expands -- the 2nd law works! Consider our comoving patch. early universe S ~ S thermal ~ today S ~ S BH ~ future S ~ S dS ~ 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 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 can’t be that hard, so our universe is (supposedly) natural. time roiling high- energy chaos today inflationary patch

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! CMB, BBN S ~ S thermal ~ today S ~ S BH ~ future S ~ S dS ~ The universe is less likely to inflate than just to look like what we see today. Inflation makes the problem worse. inflation S ~ [Penrose]

phase space sets of macroscopically indistinguishable microstates Entropy measures volumes in phase space. Boltzmann: entropy increases because there are more high- entropy states than low-entropy ones.

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. There is no clever choice of dynamics which naturally makes the early universe small, dense, and smooth. Liouville’s theorem: volume in phase space is conserved under Hamiltonian evolution. phase space 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.