Inflation in general covariant theory of gravity

TL;DR

This paper investigates inflation within Hořava-Lifshitz gravity, revealing that the universe must be flat, and analyzing how high-order spatial derivatives influence perturbations and their spectra compared to general relativity.

Contribution

It provides a detailed analysis of inflationary perturbations in Hořava-Lifshitz gravity, highlighting differences from GR due to high-order spatial derivatives and deriving explicit power spectra.

Findings

Universe is necessarily flat in this framework

Perturbations differ from GR because of high-order derivatives

Scalar and tensor spectra are nearly scale-invariant, with modified ratios

Abstract

In this paper, we study inflation in the framework of the nonrelativistic general covariant theory of the Ho\v{r}ava-Lifshitz gravity with the projectability condition and an arbitrary coupling constant $\lambda$. We find that the Friedmann-Robterson-Walker (FRW) universe is necessarily flat in such a setup. We work out explicitly the linear perturbations of the flat FRW universe without specifying to a particular gauge, and find that the perturbations are different from those obtained in general relativity, because of the presence of the high-order spatial derivative terms. Applied the general formulas to a single scalar field, we show that in the sub-horizon regions, the metric and scalar field are tightly coupled and have the same oscillating frequencies. In the super-horizon regions, the perturbations become adiabatic, and the comoving curvature perturbation is constant. We also calculate the power spectra and indices of both the scalar and tensor perturbations, and express them explicitly in terms of the slow roll parameters and the coupling constants of the high-order spatial derivative terms. In particular, we find that the perturbations, of both scalar and tensor, are almost scale-invariant, and the spectrum indices are the same as those given in GR, but the ratio of the scalar and tensor power spectra depends on the high-order spatial derivative terms, and can be different from that of GR significantly.