Vector and tensor perturbations in Horava-Lifshitz cosmology

TL;DR

This paper analyzes vector and tensor perturbations in Horava-Lifshitz cosmology, revealing that vector perturbations match general relativity and tensor modes exhibit scale-invariant spectra in the UV, with modifications in the IR.

Contribution

It derives general formulas for perturbations in Horava-Lifshitz gravity without detailed balance, including analytical power spectra in de Sitter and power-law backgrounds.

Findings

Vector perturbations are identical to those in GR.

Tensor perturbations have scale-invariant UV spectra.

Low-frequency modes are similar to GR predictions.

Abstract

We study cosmological vector and tensor perturbations in Horava-Lifshitz gravity, adopting the most general Sotiriou-Visser-Weinfurtner generalization without the detailed balance but with projectability condition. After deriving the general formulas in a flat FRW background, we find that the vector perturbations are identical to those given in general relativity. This is true also in the non-flat cases. For the tensor perturbations, high order derivatives of the curvatures produce effectively an anisotropic stress, which could have significant efforts on the high-frequency modes of gravitational waves, while for the low-frenquency modes, the efforts are negligible. The power spectrum is scale-invariant in the UV regime, because of the particular dispersion relations. But, due to lower-order corrections, it will eventually reduce to that given in GR in the IR limit. Applying the general formulas to the de Sitter and power-law backgrounds, we calculate the power spectrum and index, using the uniform approximations, and obtain their analytical expressions in both cases.