Reconstruction of f(T) Gravity with Interacting Variable-Generalised Chaplygin Gas and the Thermodynamics with Corrected Entropies

Abstract

Abstract This article reports a study on variable-generalised Chaplygin gas (VGCG) interacting with pressureless dark matter (DM) with interaction term Q chosen in the form Q=3Hδρ Λ, where ρ Λ denotes the density of the VGCG. Detailed cosmology of the interacting VGCG has been studied and a quintom behaviour of the equation of state (EoS) parameter has been observed. A statefinder analysis has shown attainment of ΛCDM fixed point by the interacting VGCG. Subsequently, a reconstruction scheme for f(T) gravity has been presented based on the interacting VGCG with power-law form of scale factor. The EoS parameter corresponding to the reconstructed f(T) has shown quintom behaviour. Finally, we have studied the generalised second law (GSL) of thermodynamics in reconstructed f(T) cosmology considering the universe as a closed bounded system with future event horizon as the cosmological boundary. We have associated two different entropies with the cosmological horizons with a logarithmic correction term and a power-law correction term. We have studied the validity of the GSL for both of these corrections.