Viability of modified gravity with Torsion-Gauss–Bonnet coupling through bouncing scenarios

The bouncing cosmological scenario provides an alternative to the standard Big Bang model by replacing the initial singularity with a smooth transition between a contracting and an expanding phase. In this paper, we center our attention in exploring the viability of bouncing cosmological scenarios in the context of [Formula: see text] gravity, an extended teleparallel framework that incorporates both the torsion scalar [Formula: see text] and the teleparallel equivalent of the Gauss–Bonnet term [Formula: see text]. A symmetric bounce cosmological model is considered, and its implications are examined by analyzing key cosmological parameters, including the Hubble parameter [Formula: see text] and the deceleration parameter [Formula: see text]. To investigate the dynamics of the bounce, we consider three different functional forms of [Formula: see text] gravity and assess the energy conditions for each model which transform singularity into bounce. Moreover, equation of state parameter [Formula: see text] is analyzed for each model to study the expansion of the universe. Furthermore, the stability and physical feasibility of the models is investigated through squared speed of sound which confirms the stability of models. The study highlights a crucial role of [Formula: see text] gravity to understand the transition from singularity to bounce.