Tsallis holographic dark energy model with observational constraints in the higher derivative theory of gravity

The present study deals with a Tsallis holographic dark energy model in a flat Friedmann-Lamatire-RbertsonWalker space-time geometry in the context of higher derivative theory of gravity. We have solved the field equations by applying energy conservation-law in non-interacting case and have obtained such a scale factor a(tau) = [sinh(root 2a(1) tau)](1/2) where a(1) is called as model parameter which shows transit phase evolution of the universe (decelerating to accelerating). Using this scale factor we have obtained the various cosmological parameters viz. Hubble parameter H, deceleration parameter (DP) q, jerk j, snap s, lerk l and max-out m. Constraining on Hubble parameters H(z) by the observational data of H(z) we have obtained the present values of H-0, a(0) and a(1) and by using these constrained values, we have studied other cosmological parameters. Taking the constant equation of state (EoS) omega(m) for ordinary matter, we have investigated the effective behaviour of various cosmological parameters and energy conditions in our model. We have observed the present values of {t(0), H-0, q(0), j(0), s(0), l(0), m(0), omega(de0), omega((eff))(0)} and discussed with Lambda CDM model. We have found the age of the present universe t(0) = 13.05 Gyrs, present value of DP q(0) = -0.8065 and transition point z(t) = 0.748 which are compatible with several observational results.