Covariant single-field formulation of effective cosmological bounces

TL;DR

This paper investigates a covariant single-field effective theory in Horndeski gravity that replaces the classical Big Bang singularity with a non-singular bounce at a critical density, maintaining the same degrees of freedom.

Contribution

It introduces a covariant single-field formulation for effective cosmological bounces within Horndeski gravity, linking bounce models to scalar-tensor theories without extra degrees of freedom.

Findings

Effective theory replaces Big Bang with a bounce at critical density.

Both effective and benchmark theories are within the same scalar-tensor class.

No additional propagating degrees of freedom are introduced.

Abstract

This study explores the feasibility of an effective Friedmann equation in removing the classical Big Bang initial singularity and replacing it with a non-singular bounce occurring at a critical energy density value. In a spatially flat, homogeneous, and isotropic universe, the effective theory is obtained by introducing a function that is parametrically dependent on the critical energy density. This function measures the deviation from the benchmark theory, which is recovered as the critical energy density approaches infinity. Focusing on the covariant single-field formulation in viable Horndeski gravity, our analysis shows that both the effective and the benchmark theories belong to the same scalar-tensor theory, without any additional propagating degrees of freedom: the cuscuton and extended cuscuton models.