On the initial singularity problem in rainbow cosmology

TL;DR

This paper critically examines the potential of rainbow cosmology to avoid the initial singularity, revealing that while it may slow the approach, it does not conclusively prevent the singularity within the semi-classical regime.

Contribution

It provides a comprehensive analysis of singularity avoidance in rainbow cosmology, considering all necessary conditions and thermodynamic implications, which previous studies overlooked.

Findings

Rainbow metrics do not conclusively avoid the initial singularity.

In semi-classical regimes, rainbow cosmology slows but does not prevent singularity.

Key questions remain unresolved near the Planck scale.

Abstract

It has been recently claimed that the initial singularity might be avoided in the context of rainbow cosmology, where one attempts to account for quantum-gravitational corrections through an effective-theory description based on an energy-dependent ("rainbow") space-time metric. We here scrutinize this exciting hypothesis much more in depth than previous analyses. In particular, we take into account all requirements for singularity avoidance, while previously only a subset of these requirements had been considered. Moreover, we show that the implications of a rainbow metric for thermodynamics are more significant than previously appreciated. Through the analysis of two particularly meaningful examples of rainbow metrics we find that our concerns are not merely important conceptually, but actually change in quantitatively significant manner the outcome of the analysis. Notably we only find examples where the singularity is not avoided, though one can have that in the regime where our semi-classical picture is still reliable the approach to the singularity is slowed down when compared to the standard classical scenario. We conclude that the study of rainbow metrics provides tantalizing hints of singularity avoidance but is inconclusive, since some key questions remain to be addressed just when the scale factor is very small, a regime which, as here argued, cannot be reliably described by an effective rainbow-metric picture.