Detailed balance in Horava-Lifshitz gravity

TL;DR

This paper explores Horava-Lifshitz gravity with a scalar field under detailed balance, revealing complex interactions, potential for inflation, and discussing the necessity to possibly abandon detailed balance for consistency.

Contribution

It introduces a scalar-tensor extension of Horava-Lifshitz gravity with detailed balance, analyzing its implications for ultraviolet stability and cosmological inflation.

Findings

Scalar field can produce a scale-invariant spectrum for inflation

The theory includes a new gravitational term for stability

No Einstein frame analog exists in this model

Abstract

We study Horava-Lifshitz gravity in the presence of a scalar field. When the detailed balance condition is implemented, a new term in the gravitational sector is added in order to maintain ultraviolet stability. The four-dimensional theory is of a scalar-tensor type with a positive cosmological constant and gravity is nonminimally coupled with the scalar and its gradient terms. The scalar field has a double-well potential and, if required to play the role of the inflation, can produce a scale-invariant spectrum. The total action is rather complicated and there is no analog of the Einstein frame where Lorentz invariance is recovered in the infrared. For these reasons it may be necessary to abandon detailed balance. We comment on open problems and future directions in anisotropic critical models of gravity.