Nonpropagation of scalar in the deformed Ho\v{r}ava-Lifshitz gravity

TL;DR

This paper investigates the behavior of a scalar mode in deformed Hořava-Lifshitz gravity and finds it does not propagate in Minkowski spacetime without gauge fixing.

Contribution

It demonstrates that the scalar trace mode is nonpropagating in Minkowski background without gauge fixing, clarifying the physical degrees of freedom in this gravity model.

Findings

Scalar mode does not propagate in Minkowski spacetime

No gauge fixing needed to identify physical degrees of freedom

Constraints eliminate the scalar's propagation

Abstract

We study the propagation of a scalar, the trace of $h_{ij}$ in the deformed Ho\v{r}ava-Lifshitz gravity with coupling constant $\lambda$. It turns out that this scalar is not a propagating mode in the Minkowski spacetime background. In this work, we do not choose a gauge-fixing to identify the physical degrees of freedom and instead, make it possible by substituting the constraints into the quadratic Lagrangian.