  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.
