On the Signature of Short Distance Scale in the Cosmic Microwave Background

TL;DR

This work demonstrates that short-distance physics during inflation can imprint on the cosmic microwave background not only through the usual $(H/M)^2$ suppression but also via a second, nontrivial expansion in $rac{\dot{\phi}^2}{M^4}$, arising from higher-order kinetic terms in a locally defined action $p(X,\phi)=F(X)-V(\phi)$. By developing slow-roll background and perturbation theory with a general $F(X)$, it shows that the scalar fluctuation spectrum depends on a sound speed $c_s$ and horizon-crossing conditions $c_s k=aH$, leading to potentially observable deviations from the standard predictions. Through concrete examples, notably chaotic inflation with $F(X)=X+\frac{\alpha}{M^4}X^2$ and other potentials, the paper demonstrates that these short-distance effects can be substantial even for $H\ll M$ and can exhibit non-analytic dependence on the new physics scale $M$. The results highlight model-dependent signatures in the CMB and suggest that future observations could probe the scale of short-distance physics via inflationary perturbations.

Abstract

We discuss the signature of the scale of short distance physics in the Cosmic Microwave Background. In addition to effects which depend on the ratio of Hubble scale H during inflation to the energy scale M of the short distance physics, there can be effects which depend on $\dotφ^2/M^4$ where $φ$ is the {\it classical background} of the inflaton field. Therefore, the imprints of short distance physics on the spectrum of Cosmic Microwave Background anisotropies generically involve a {\it double expansion}. We present some examples of a single scalar field with higher order kinetic terms coupled to Einstein gravity, and illustrate that the effects of short distance physics on the Cosmic Microwave Background can be substantial even for H << M, and generically involve corrections that are not simply powers of H/M. The size of such effects can depend on the short distance scale non-analytically even though the action is local.