Implications of a holographic density of states on inflation

TL;DR

This paper explores how a holographic density of states, indicating fewer degrees of freedom at high energies, could influence inflationary models by altering the spectral index of quantum fluctuations, potentially observable near the Planck scale.

Contribution

It introduces a novel effect of holographic degrees of freedom thinning on inflation, predicting a positive power correction to the spectral index of fluctuations.

Findings

Thinning of degrees of freedom affects the spectral index.

Predicts a positive power correction to the spectral index.

Potential observational signatures near the Planck scale.

Abstract

There is theoretical evidence that the number of degrees of freedom in quantum fields decreases as one studies them at extremely short distances. This emerges from the study of entropy of black holes, as well as from holographic theories in AdS geometries. Presumably a theory of quantum gravity will provide an explicit description of how the number of degrees of freedom thin out as one studies high energy scales. We do not have a comprehensive theory of how such a thinning of degrees of freedom would occur. It is likely that there might be residual (and measurable) effects at larger length scales, though this might be significant only near the Planck scale. There are very few instances in Nature where one might be able to see effects of this thinning. One promising venue is in the phenomenon of inflation, produced in the simplest models through a scalar inflaton field in a potential with a flat ("slow-roll") part as well as a potential well. We compute the effect of such a thinning of degrees of freedom upon the running of the spectral index of quantum fluctuations of the inflaton and deduce that this will lead to a positive power of wave-vector (opposite to the usual $\sim -\epsilon$, i.e., negative power correction). Some comments are then made about the impact on observations (or non-observations) of such fluctuations \cite{Martin}.