Cosmological bouncing solutions and their stability in teleparallel gravity
The cosmological dynamics in the early universe are investigated to explore the possibility of the sign reversal of the Hubble parameter as a key feature of non-singular bouncing cosmological solutions in higher-order torsion gravity. The self-consistent multiple cosmological regimes are studied, such as the accelerated expansion, ultra-relativistic, radiation-dominated, sub-relativistic, dust, and stiff matter phases, for three distinct parametrizations of the scale factor: power-law, exponential, and hybrid forms. In particular, five characteristic bouncing scenarios are analyzed: symmetric bounce, super-bounce, oscillatory bounce, matter bounce, and Type IV singularity-free bounce, so that the gravitational Lagrangian can be reconstructed to satisfy bounce conditions at the bounce time. It is found that each scenario requires a violation of the null energy condition, implying the presence of exotic matter with an effective equation of state to drive both the bounce and late-time cosmic acceleration. As a result, it is explicitly demonstrated that higher-order torsion gravity naturally incorporates the bouncing solutions without introducing ad hoc matter fields, providing a possible geometric framework for non-singular early universe evolution. Furthermore, the consistency of the bouncing solutions with the observational constraints of the cosmic microwave background and gravitational wave spectrum is shown, while offering testable predictions for primordial perturbations.