  We explore the change in the sign of the Hubble parameter in the early
universe and its stability in higher-order torsion gravity. Our study explores
the various scenarios involving the sub-relativistic universe, radiation
universe, ultra-relativistic universe, dust universe, and stiff fluid universe.
Different analytical methods, including power-law, exponential scalar factor,
and hybrid scale factor methods, are employed to examine the behavior of the
universe about the equation of state (EoS) parameters. This study is based on
the previous ones by presenting a more comprehensive analysis of the bouncing
scenarios within the higher-order torsion gravity framework. It makes
significant progress in reconstructing gravitational Lagrangians, which are
tailored to specific parameter values, allowing for a thorough examination of
the energy conditions necessary for successful bouncing models. These derived
Lagrangians provide analytical solutions for a range of bouncing models,
including symmetric bounce, super-bounce, oscillatory bounce, matter bounce,
and exponential bouncing settings. The presence of exotic matter is responsible
for the accelerated expansion of the universe, as it exhibits substantial
negative pressure. A thorough analysis of torsion-based gravity theories and
the specific investigations into bouncing scenarios set it apart from previous
works exploring alternative gravity theories and their cosmological
consequences. These contributions lie in the comprehensive exploration of
bouncing models and the detailed examination of the energy conditions in
higher-order torsion gravity.
