Singularity avoidance in rainbow cosmology

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 analyse this picture in detail in an attempt to present a more rigorous description of the problem. In particular, we show that the implications of a rainbow metric for thermodynamics are more significant than previously appreciated. We show two particularly meaningful examples where the singularity is not avoided suggesting that, although the rainbow-metric scenario provides tantalizing hints of singularity avoidance, it 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.