Non-singular bouncing model in energy momentum squared gravity

This work is concerned to study the bouncing nature of the Universe for an isotropic configuration of fluid T-alpha beta and Friedmann-Lemaitre-Robertson-Walker metric scheme. This work is carried out under the novelf (g, T alpha beta T alpha beta ) gravitation by assuming a specific model i.e. f (g, T-2) = g+ alpha g + 2 lambda T-2 with alpha and lambda are constants, serving as free parameters. The terms g and T-2 served as an Gauss-Bonnet invariant and square of the energy-momentum trace term as an inclusion in the gravitational action respectively, and is proportional to T-2 = T alpha beta T alpha beta. A specific functional form of the Hubble parameter is taken to provide the evolution of cosmographic parameters. A well known equation of state parameter, omega(t)= -k logt(t +epsilon)/ t - 1 is used to represent the dynamical behavior of energy density, matter pressure and energy conditions. A detailed graphical analysis is also provided to review the bounce. Furthermore, all free parameters are set in a way, to make the supposed Hubble parameter act as the bouncing solution and ensure the viability of energy conditions. Conclusively, all necessary conditions for a bouncing model are checked.