Primordial perturbations in a rainbow universe with running Newton constant

TL;DR

This paper investigates how a running Newton constant in a rainbow universe affects primordial perturbations, showing that specific conditions on G are needed to match observations and address the horizon problem.

Contribution

It introduces a model with a running Newton constant in a rainbow universe and analyzes its impact on the spectral index of primordial perturbations.

Findings

Only when G tends to zero can the observed spectral index be matched.

Vacuum perturbations allow both accelerating and decelerating expansion.

Thermal perturbations require decelerating expansion.

Abstract

We compute the spectral index of primordial perturbations in a rainbow universe. We allow the Newton constant $G$ to run at (super-)Planckian energies and we consider both vacuum and thermal perturbations. If the rainbow metric is the one associated to a generalized Horava-Lifshitz dispersion relation, we find that only when $G$ tends asymptotically to zero can one match the observed value of the spectral index and solve the horizon problem, both for vacuum and thermal perturbations. For vacuum fluctuations the observational constraints imply that the primordial universe expansion can be both accelerating or decelerating, while in the case of thermal perturbations only decelerating expansion is allowed.