What does inflation really predict?

Abstract

If the inflaton potential has multiple minima, as may be expectedin, e.g., the string theory ‘landscape’, inflation predicts a probabilitydistribution for the cosmological parameters describing spatial curvature(Ωtot), darkenergy (ρΛ,w etc), the primordialdensity fluctuations (Q, ns,d ns/d ln k etc) and primordialgravitational waves (r, nt etc). We compute this multivariate probability distribution for variousclasses of single-field slow-roll models, exploring its dependence on thecharacteristic inflationary energy scales, the shape of the potentialV and the choice of measure underlying the calculation. We find that unless the characteristic scaleΔϕ onwhich V varies happens to be near the Planck scale, the only aspect ofV that matters observationally is the statistical distribution of its peaks and troughs. For allenergy scales and plausible measures considered, we obtain the predictions , w = −1 and ρΛ in the observed ballpark but uncomfortably high. The high energy limit predicts, , and , consistent with observational data and indistinguishable from eternal inflation. The low energy limit predicts five parameters but favours largerQ andredder ns than observed. We discuss the coolness problem, the smoothness problem and the potholeparadox, which severely limit the viable class of models and measures. Predictionsinsensitive to pre-inflationary conditions can arise either from eternal inflation attractorbehaviour or from anthropic selection effects probing merely a tiny non-special part of theinitial distribution. We argue that these two mechanisms are severely challenged by thecoolness problem and the smoothness problem, respectively. Our findings bode well fordetecting an inflationary gravitational wave signature with future CMB polarizationexperiments, with the arguably best-motivated single-field models favouring the detectablelevel .