Cosmology of Tsallis holographic scalar field models in Chern–Simons modified gravity and optimization of model parameters through χ 2 minimization

Abstract

Abstract The present study reports reconstruction schemes for tachyon, k-essence and dilaton scalar field model of Dark Energy (DE) through Tsallis holographic dark fluid under the framework of Chern–Simons modified gravity. Reproducing the conservation equation for a coupled model with interaction term Q = 3 H b 2 ρ m $Q=3H{b}^{2}{\rho }_{m}$ we have reconstructed the different scalar fields and the corresponding potentials. In the case of tachyon, ΛCDM fixed point is attained under this cosmological settings. Considering k-essence in this interacting situation, we have derived some constraints on the interaction term as well as Tsallis holographic dark energy parameter. Reconstructing dilaton scalar field, we have studied the behavior of scalar field and potential. In all those cases, the reconstructed Equation of State (EoS) parameters have been plotted and when computed for current universe z = 0 are found to be consistent with various observational data including Planck + WP + BAO. The only exception is a particular case of reconstructed k-essence model where phantom behavior is apparent, but its numerical value is deviated from the bounce set by the observations. Expressions for different constraints have been obtained and evolutionary behavior of reconstructed scalar fields and potentials for the various cases have been pictorially presented. Finally, we have developed a functional relationship between Hubble parameter and redshift and optimized the parameter values through χ 2 minimization using the observed Hubble parameter values from Hai Yu et al. 2018 ApJ 856 3.