Parametrization of Hubble parameter in f̂(𝒯 ,𝒯G) gravity model with tachyon field

Abstract

We look into the cosmological uses of the new modified gravitational theory [Formula: see text], which is based on the torsion invariant [Formula: see text] and the teleparallel equivalent of the Gauss–Bonnet term [Formula: see text]. The corresponding cosmology of [Formula: see text] gravity is very intriguing because it varies from both [Formula: see text] theories and the [Formula: see text] class of curvature-modified gravity. In this paper, we have investigated the applicability of an alternative gravitational theory called [Formula: see text] by applying the energy conditions. Here, we assumed the form of [Formula: see text], where [Formula: see text] and [Formula: see text] are arbitrary constants. We have examined the cosmological applications of [Formula: see text] gravity. Here, we consider two particular expressions of the time-dependent Hubble parameter. Both the model parameters are constrained jointly by the Observation Hubble dataset (OHD), the Pantheon dataset and the BAO data to constrain the model parameters using the Markov Chain Monte Carlo (MCMC) minimization technique. We determine the present values of Hubble constant for model [Formula: see text]: [Formula: see text], [Formula: see text] and [Formula: see text]; and model [Formula: see text]: [Formula: see text], [Formula: see text] and [Formula: see text] for the OHD+BAO+Pantheon dataset. Using the most recent estimated values of Hubble parameter, we properly analyzed the energy conditions and looked at the final behavior of our model. Additionally, we have explored the [Formula: see text] plane and also we have extracted the scalar field as well as potential of [Formula: see text] gravity and its relationship to the tachyon field. In addition, we find that, depending on the model parameters, the dark energy (DE) equation-of-state (EoS) parameter may be quintessence or phantom-like, or it may undergo phantom-divide crossing. Finally, we find that all the essential features of the model are satisfied successfully.