A note on Friedmann equation of FRW universe in deformed Horava-Lifshitz gravity from entropic force

TL;DR

This paper derives the Friedmann equation for an FRW universe within deformed Hořava-Lifshitz gravity using Verlinde's entropic gravity approach, showing consistency with Einstein gravity in a specific limit.

Contribution

It applies the entropic gravity framework to deformed Hořava-Lifshitz gravity and derives the corresponding Friedmann equation, highlighting its reduction to Einstein gravity under certain conditions.

Findings

Friedmann equation obtained from entropic gravity in deformed Hořava-Lifshitz gravity.

Consistency with Einstein gravity as the deformation parameter approaches infinity.

Supports the validity of entropic gravity interpretation in this modified gravity context.

Abstract

With entropic interpretation of gravity proposed by Verlinde, we obtain the Friedmann equation of the Friedmann-Robertson-Walker universe for the deformed Ho\v{r}ava-Lifshitz gravity. It is shown that, when the parameter of Ho\v{r}ava-Lifshitz gravity $\omega\rightarrow \infty$, the modified Friedmann equation will go back to the one in Einstein gravity. This results may imply that the entropic interpretation of gravity is effective for the deformed Ho\v{r}ava-Lifshitz gravity.