Cosmology of new Tsallis holographic dark energy-based reconstructed models in teleparallel theories

Abstract

Reconstruction of Lagrangian functions present in the action of modified gravity theories is one of the most captivating subjects in recent cosmology. This paper reconstructs the form of Lagrangian function of some teleparallel theories based on a recently proposed holographic dark energy model namely new Tsallis HDE. For this purpose, we assume ordinary matter contents as perfect fluid with background geometry as flat FRW spacetime. On the first place, we reconstruct [Formula: see text] function by taking some well-known IR cutoff choices into account like Hubble radius, event horizon, Granda–Oliveros cutoff and conformal time as different cases. Moreover, we consider two entropy corrected forms of new Tsallis HDE with the simplest choice for IR cutoff. We explore the graphical behavior of different cosmic quantities, e.g. dark energy EoS parameter, the generalized second law of thermodynamics, the null energy condition, speed of sound and trajectories in [Formula: see text] plane for these reconstructed solutions and discuss their viability. Then we extend our work to [Formula: see text] theory and reconstruct the Lagrangian function for new Tsallis HDE with three simple choices of IR cutoff (Hubble radius and event horizon), and Granda–Oliveros cutoff and discuss the significance of obtained solutions graphically through same cosmic measures. It is found that presented models are consistent with the recent cosmic data values, however, stability can be achieved in some certain cases only.