# General Modified Friedmann Equations in Rainbow Flat Universe, by Thermodynamics

## TL;DR

This paper explores deriving Friedmann equations in Rainbow gravity using thermodynamics without assuming constant rainbow functions, revealing that classical and quantum entropy corrections alone are insufficient for flat FRW metrics.

## Contribution

It demonstrates that non-constant rainbow functions require additional considerations beyond standard thermodynamic relations to derive Friedmann equations in Rainbow gravity.

## Key findings

- Classical entropy-area relation is insufficient for flat FRW in Rainbow gravity.
- Quantum logarithmic corrections do not fully resolve the derivation issue.
- Constant rainbow functions simplify the derivation process.

## Abstract

We investigate the derivation of Friedmann equations in Rainbow gravity following Jacobson thermodynamic approach. We do not restrict the rainbow functions to be constant as is customarily used, and show that the first law of thermodynamics with a corresponding `classical' proportionality between entropy and surface area, supplemented eventually by a `quantum' logarithmic correction, are not in general sufficient to obtain the equations in flat FRW metrics.