Reconstructing the k-essence and the dilation field models of the THDE in f(R, T) gravity

Abstract

Inspired by the work of Chattopadhyay et al. (Eur Phys J C 74(9):3080, 2014. https://doi.org/10.1140/epjc/s10052-014-3080-3 ) and Yang et al. (Mod Phys Lett A 26:191, 2011. https://doi.org/10.1142/S0217732311034682 ), we examine the energy density explained via $$\rho _{\Lambda }=3\beta ^{2}M^{2}_{p}H^{-2\delta +4}$$ for the Tsallis holographic dark energy (THDE) model in the framework of f(R, T) gravity. In the structure of f(R, T) gravity, the correspondence between the scalar-field models of the k-essence and the dilation with the THDE is investigated by us. The correspondence among the Tsallis holographic density with the k-essence and the dilation densities permits the reconstruction of the dynamics and the potentials for the k-essence and the dilation field models, in a flat FRW (Friedman–Robertson–Walker) Universe. We have reconstructed the Tsallis holographic k-essence and the dilation fields models in the region $$\omega _{\Lambda } >-1$$ for the EoS parameter for the different Tsallis parameter $$\delta $$ . By investigation, we observe that for the THDE k-essence and the dilation models, the accelerated expansion can be obtained in the f(R, T) gravity if the related parameters satisfy some constraints.