Detailed balance condition and ultraviolet stability of scalar field in Horava-Lifshitz gravity

TL;DR

This paper demonstrates that the scalar field in Horava-Lifshitz gravity can be stabilized by softly breaking the detailed balance condition, preserving some of its attractive features and reducing coupling constants.

Contribution

It shows that the detailed balance condition can be softly broken to achieve ultraviolet stability of scalar fields in various Horava-Lifshitz gravity models.

Findings

Scalar field stabilization with softly broken detailed balance.

Reduction in independent coupling constants.

Existence of a master equation for scalar perturbations.

Abstract

Detailed balance and projectability conditions are two main assumptions when Horava recently formulated his theory of quantum gravity - the Horava-Lifshitz (HL) theory. While the latter represents an important ingredient, the former often believed needs to be abandoned, in order to obtain an ultraviolet stable scalar field, among other things. In this paper, because of several attractive features of this condition, we revisit it, and show that the scalar field can be stabilized, if the detailed balance condition is allowed to be softly broken. Although this is done explicitly in the non-relativistic general covariant setup of Horava-Melby-Thompson with an arbitrary coupling constant $\lambda$, generalized lately by da Silva, it is also true in other versions of the HL theory. With the detailed balance condition softly breaking, the number of independent coupling constants can be still significantly reduced. It is remarkable to note that, unlike other setups, in this da Silva generalization, there exists a master equation for the linear perturbations of the scalar field in the flat Friedmann-Robertson-Walker background.