Covariant single-field formulation of effective cosmological bounces

This study explores the feasibility of an effective Friedmann equation in removing the classical initial Big Bang singularity, replaced by a 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 parametrically dependent on the critical energy density. It measures the deviation from the benchmark theory characterising the asymptotic behaviour 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, with no additional propagating degrees of freedom: the cuscuton and extended cuscuton models.