The dynamical system analysis of the cosmological models in f (T, T ) gravity, where T and T respectively represents the torsion scalar and trace of the energy-momentum tensor has been investigated. It demonstrates how first-order autonomous systems can be treated as cosmological equations and analyzed using standard dynamical system theory techniques. Two forms of the function f (T, T ) are considered (i) one with the product of trace and higher order torsion scalar and the other (ii) linear combination of linear trace and squared torsion. For each case, the critical points are derived and their stability as well the cosmological behaviours are shown. In both the models the stable critical points are obtained in the de-Sitter phase whereas in the matter and radiation dominated phase unstable critical points are obtained. At the stable critical points, the deceleration parameter shows the accelerating behaviour of the Universe whereas the equation of state parameter shows the ΛCDM behaviour. Finally the obtained Hubble parameter of the models are checked for the cosmological data sets.
In this paper, we have studied the bouncing behaviour of the cosmological models formulated at the background of Hubble function in F(R, G) theory of gravity, where R and G respectively denotes the Ricci scalar and Gauss-Bonnet invariant. The actions of bouncing cosmology are studied under consideration of different viable models and can resolve the difficulty of singularity in standard Big-Bang cosmology. Both the models are showing bouncing behaviour and satisfying the bouncing cosmological properties. Models based on dynamical, deceleration, and energy conditions indicate the accelerating behavior at the late evolution time. Phantom at the bounce epoch is analogous to a quintessence behavior. Finally, we formulate the perturbed evolution equations and investigate the stability of two bouncing solutions.
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