A New Extension of Ho\v{r}ava-Lifshitz Gravity and Curing Pathologies of the Scalar Graviton

TL;DR

This paper introduces an extended Hořava-Lifshitz gravity model with additional conformal symmetry and a scalar field, which alleviates known scalar graviton pathologies such as ghosts and instabilities.

Contribution

It develops a new scalar-tensor extension of HL gravity with residual global Weyl symmetry that avoids common scalar graviton issues.

Findings

No ghost or instability problems up to cubic order.

Reduces to HL gravity under specific parameter choices.

Perturbation analysis confirms improved stability.

Abstract

We consider an extension of the Ho\v{r}ava-Lifshitz gravity with extra conformal symmetry by introducing a scalar field with higher order curvature terms. Relaxing the exact local Weyl symmetry, we construct an action with three free parameters which breaks local anisotropic Weyl symmetry but still preserves residual global Weyl symmetry. At low energies, it reduces to a Lorentz-violating scalar-tensor gravity. With a constant scalar field background and particular choices of the parameters, it reduces to the Ho\v{r}ava-Lifshitz (HL) gravity, but any perturbation from these particular configurations produces some non-trivial extensions of HL gravity. The perturbation analysis of the new extended HL gravity in the Minkowski background shows thatthe pathological behaviors of scalar graviton, i.e., ghost or instability problem, and strong coupling problem do not emerge up to cubic order as well as quadratic order.