# Generalized uncertainty principle and Ho\v{r}ava-Lifshitz gravity

## TL;DR

This paper investigates the relationship between the generalized uncertainty principle and modified Hořava-Lifshitz gravity, revealing similarities in graviton propagators and highlighting differences due to specific tensor contributions.

## Contribution

It establishes a connection between GUP and HL gravity by replacing the GUP density with a cutoff function, and compares the resulting graviton propagators.

## Key findings

- GUP-corrected graviton propagators resemble HL tensor propagators
- The $p^5$-term from Cotton tensor is absent in GUP corrections
- GUP and HL gravity share qualitative features in graviton behavior

## Abstract

We explore a connection between generalized uncertainty principle (GUP) and modified Ho\v{r}ava-Lifshitz (HL) gravity. The GUP density function may be replaced by the cutoff function for the renormalization group of modified Ho\v{r}ava-Lifshitz gravity. We find the GUP-corrected graviton propagators and compare these with tensor propagators in the HL gravity. Two are qualitatively similar, but the $p^5$-term arisen from Cotton tensor is missed in the GUP-corrected graviton propagator.