Rainbow gravity and scale-invariant fluctuations

TL;DR

This paper explores how rainbow gravity theories with modified dispersion relations can produce scale-invariant cosmological fluctuations without inflation, highlighting gravity's behavior at high energies and its relation to dimensional reduction.

Contribution

It demonstrates that rainbow gravity can naturally generate scale-invariant fluctuations and explains the high-energy behavior of gravity during dimensional reduction.

Findings

Gravity effectively switches off at high energies in rainbow gravity.

Scale-invariance arises without horizon scales due to gravity's conformal coupling.

Deviations from exact scale invariance relate to esoteric inflation in the rainbow frame.

Abstract

We re-examine a recently proposed scenario where the deformed dispersion relations associated with a flow of the spectral dimension to a UV value of 2 leads to a scale-invariant spectrum of cosmological fluctuations, without the need for inflation. In that scenario Einstein gravity was assumed. The theory displays a wavelength-dependent speed of light but by transforming to a suitable "rainbow frame" this feature can be removed, at the expense of modifying gravity. We find that the ensuing rainbow gravity theory is such that gravity switches off at high energy (or at least leads to a universal conformal coupling). This explains why the fluctuations are scale-invariant on all scales: there is no horizon scale as such. For dispersion relations that do not lead to exact scale invariance we find instead esoteric inflation in the rainbow frame. We argue that these results shed light on the behaviour of gravity under the phenomenon of dimensional reduction.