Bimetric varying speed of light theories and primordial fluctuations

TL;DR

This paper introduces a bimetric varying speed of light theory that naturally generates primordial density fluctuations, providing a simple and universal solution to structure formation and cosmological problems.

Contribution

It demonstrates that bimetric VSL theories with a Dirac-Born-Infeld type K-essence can produce scale-invariant fluctuations and offers a novel non-perturbative understanding of the bi-scalar dynamics.

Findings

DBI K-essence models produce near scale-invariant fluctuations.

The full bimetric structure simplifies to a bi-scalar driven by cosmological constants.

Bimetric VSL theories address multiple cosmological problems and causality issues.

Abstract

We exhibit a varying speed of light (VSL) theory that implements the recently proposed decaying speed of sound mechanism for generating density fluctuations. We avail ourselves of bimetric VSL theories, where the speed of gravity differs from that of light. We first show that a Dirac-Born-Infeld (DBI) type of $K$-essence has the necessary speed of sound profile to produce (near) scale-invariant fluctuations. We then examine the map between bimetric and $K$-essence models: typically the bi-scalar connecting the two metrics is a $K$-essence field in one of them. Remarkably, the DBI model is found to perturbatively represent the minimal bimetric model, where the bi-scalar is Klein-Gordon in the matter frame. But the full non-perturbative bimetric structure is even simpler: the bi-scalar dynamics should be simply driven by a cosmological constant in the matter frame, balanced by an opposite cosmological constant in the gravity frame. Thus the problem of structure formation receives an elegant and universal solution within bimetric VSL theories, which are known to also solve the flatness and entropy problems and evade a plethora of causality concerns.