Scale Invariant Spectrum from Variable Speed of Light Metric in a Bimetric Gravity Theory

TL;DR

This paper derives a scale-invariant spectrum from a bimetric gravity theory with variable speed of light, matching CMB observations and solving horizon and flatness problems.

Contribution

It introduces a novel bimetric gravity model with VSL that produces a nearly scale-invariant spectrum consistent with observations.

Findings

Scalar spectral index n_s ≈ 0.97

Running of spectral index α_s ≈ -5×10^{-4}

Horizon and flatness problems are solved

Abstract

An approximately scale invariant spectrum generating the seeds of structure formation is derived from a bimetric gravity theory. By requiring that the amplitude of the CMB fluctuations from the model matches the observed value, we determine the fundamental length scale in the model to be a factor of 10^5 times larger than the Planck length, which results in a scalar mode spectral index: n_s\approx 0.97, and its running: \alpha_s\approx -5\times 10^{-4}. This is accomplished in the variable speed of light (VSL) metric frame, in which the dynamics of perturbations of the bimetric scalar field are determined by a minimally-coupled Klein-Gordon equation, and it is assumed that modes are born in a ground state at a scale given by the fundamental length scale appearing in the bimetric structure. We show that while this is taking place for scales of interest, the background (primordial) radiation energy density is strongly suppressed as a result of the bimetric structure of the model. Nevertheless, the enlarged lightcone of matter fields ensures that the horizon and flatness problems are solved.