Description
We investigate a range of non-singular cosmological scenarios within the framework of Horndeski gravity. In particular, we construct a bouncing Universe model and propose a minimal setup that realizes a non-pathological Genesis scenario. Both constructions allow for a fully stable transition to the kination epoch, during which General Relativity (GR) is restored. These scenarios successfully evade the no-go theorem, almost at the expense of potential strong-coupling issues in the early phase. The requirement of strong-coupling avoidance imposes strict constraints on the model parameters and, in certain cases, forbids the generation of a red-tilted scalar spectrum. Furthermore, we explore an alternative scenario in which the Genesis phase precedes a period of Starobinsky inflation. We show that the corrections from the Genesis phase can naturally account for the recent ACT observations. Based on: 2207.04071, 2503.02626, 2509.04832, 2601.14008