Horava-Lifshitz gravity with $\lambda\to\infty$

TL;DR

This paper investigates the behavior of Horava-Lifshitz gravity as the parameter λ approaches infinity, analyzing quantum fluctuations and stability in a cosmological setting to identify its potential as an ultraviolet fixed point.

Contribution

It provides a detailed analysis of the λ→∞ limit in Horava-Lifshitz gravity, demonstrating finite quantum fluctuations and conditions for weak coupling.

Findings

Quantum fluctuation amplitudes remain finite as λ→∞

The theory remains weakly coupled under specific conditions

Supports λ→∞ as a candidate for the UV fixed point

Abstract

In the framework of the power-counting renormalizable theory of gravitation, recently proposed by Ho\v{r}ava, we study the limit $\lambda\to\infty$, which is arguably the most natural candidate for the ultraviolet fixed point of the renormalization group flow. In the projectable version with dynamical critical exponent $z=3$, we analyze the Friedmann-Robertson-Walker background driven by the so-called "dark matter as integration constant" and perturbations around it. We show that amplitudes of quantum fluctuations for both scalar and tensor gravitons remain finite in the limit and that the theory is weakly coupled under a certain condition.