Exact cosmological bouncing solutions in f(T,TG) gravity

The f(T, TG) f ( T , T G ) gravity theory is an extension of general relativity that incorporates the torsion scalar T T as well as the teleparallel equivalent to the Gauss-Bonnet term TG T G , to explore early and late time universe cosmology beyond the standard model. In this work, we obtain exact solutions of the field equations in the framework of f(T, TG) f ( T , T G ) gravity in the context of cosmological bouncing scenarios. For this, we explore the non-singular evolution of the universe by considering various bouncing cosmological models characterized by different scale factors such as the symmetric bounce, oscillatory bounce, superbounce, matter bounce, and singular bounce scenarios. For each scale factor model, we obtained the functional form of f(T, TG) f ( T , T G ) defining different ansatz like g(T)+h(TG),~TG~g(T) g ( T ) + h ( T G ) , T G g ( T ) and T+TG ~g(T) T + T G g ( T ) that satisfy the modified field equations and yields viable cosmological solutions. The analytical behaviors of the scale factor, Hubble parameter, energy density and pressure are examined to discuss the nature of the bounce and the avoidance of initial singularities. Our results demonstrate that the f(T, TG) f ( T , T G ) framework provides consistent and physically acceptable bouncing cosmologies capable of describing a smooth transition from contraction to expansion, thereby offering a viable alternative to inflationary models for the early universe.