What does inflation really predict?

Abstract

If the inflaton potential has multiple minima, as may be expected in, e.g., the string theory "landscape", inflation predicts a probability distribution for the cosmological parameters describing spatial curvature (Ωtot), dark energy (ρΛ, w, etc.), the primordial density fluctuations (Q, ns, dns/d ln k, etc.) and primordial gravitational waves (r, nt, etc.). We compute this multivariate probability distribution for various classes of single-field slow-roll models, exploring its dependence on the characteristic inflationary energy scales, the shape of the potential V and and the choice of measure underlying the calculation. We find that unless the characteristic scale ∆φ on which V varies happens to be near the Planck scale, the only aspect of V that matters observationally is the statistical distribution of its peaks and troughs. For all energy scales and plausible measures considered, we obtain the predictions Ωtot ≈ 1 ± 10 −5 , w = −1 and ρΛ in the observed ballpark but uncomfortably high. The high energy limit predicts ns ≈ 0.96, dns/d ln k ≈ −0.0006, r ≈ 0.15 and nt ≈ −0.02, consistent with observational data and indistinguishable from eternal V ∝ φ 2 inflation. The low-energy limit predicts 5 parameters but prefers larger Q and redder ns than observed. We discuss the coolness problem, the smoothness problem and the pothole paradox, which severely limit the viable class of models and measures. Predictions insensitive to pre-inflationary conditions can arise either from eternal inflation attractor behavior or from anthropic selection effects probing merely a tiny non-special part of the initial distribution. We argue that these two mechanisms are severely challenged by the coolness problem and the smoothness problem, respectively. Our findings bode well for detecting an inflationary gravitational wave signature with future CMB polarization experiments, with the arguably best-motivated single-field models favoring the detectable level r ∼ 0.03.

Inflation and String Theory

“…Although numerical experiments in the particular example of warped Dbrane inflation (see §5.1) give strong evidence that six fields can be large enough for universality to take hold [240,535], much remains to be learned about the statistics of general multi-field models -see [255,488,[536][537][538][539][540][541][542] for related work.…”

Probabilities in the inflationary multiverse

“…Readers who dislike anthropic arguments are encouraged to think in terms of reference classes of their own choice. t [11,12]; see also [13,14] for a recent discussion.) The reason for the cutoff dependence of probabilities is that the volume of an eternally inflating universe is growing exponentially with time.…”

Supersymmetric and smooth hybrid inflation in the light of WMAP3

“…[16] for a recent review of progress in defining probabilities in an eternally inflating spacetime, and Ref. [17] for discussion and computational examples.…”