Observational predictions of inflationary model in spatially covariant gravity with two tensorial degrees of freedom for gravity

TL;DR

This paper explores an inflationary model based on spatially covariant gravity with two tensorial degrees of freedom, analyzing its theoretical structure and observational predictions like the spectral index and tensor-to-scalar ratio.

Contribution

It extends the conditions for two tensorial degrees of freedom to include scalar fields and applies this framework to inflation, providing new insights into inflationary predictions.

Findings

Tensor-to-scalar ratio can be order unity or small depending on model parameters.

The model's predictions for spectral index align with observational constraints.

Conditions for two tensorial degrees of freedom are generalized to scalar field scenarios.

Abstract

We study the inflationary model constructed from a Spatially Covariant Gravity (SCG). The Lagrangian for the SCG in our consideration is expressed as the polynomial of irreducible SCG monomials where the total number of derivatives of each monomial is two, and the theory propagates two tensorial degrees of freedom of gravity up to the first order in cosmological perturbations. The condition for having two tensorial degrees of freedom studied earlier in literature for such theories is derived in vacuum. We extend the condition for having two tensorial degrees of freedom to the case where a scalar field is included by imposing a gauge-fixing. We apply the resulting SCG to describe inflationary universe. The observational predictions such as the scalar spectral index and tensor-to-scalar ratio from this model are investigated. We find that the tensor-to-scalar ratio in this model can either be in the order of unity or be small depending on the parameter of the model.