Physical acceptability of modified Rényi holographic dark energy cosmological model in \({\varvec{f}}\left( {{\varvec{T}},\user2{\mathcal{B}}} \right)\) theory of gravitation

Abstract

In this study, we consider a modified dark energy model in the framework of \(f\left( {T,\;\mathcal{B}} \right)\) gravity theory, where T is the torsion scalar, and \(\mathcal{B}\) is the boundary term of spacetime. The model we consider is the LRS Bianchi type-I spacetime in the presence of modified Rényi holographic dark energy and pressureless matter. To solve the field equations and obtain a deterministic solution, we contemplate the simple form of \(f\left( {T, \;\mathcal{B}} \right)\) gravity as \(f\left( {T,\mathcal{B}} \right) = \alpha \mathcal{B}^{\beta } + T\) and the emergent scale factor. We calculated the cosmological parameters to study the behaviour of the Universe during cosmic evolution. The reconstructed dark energy sector has been compared with observations of BAO, SNe, and certain galaxy lensing, as well as Planck-based \({\Lambda }\)CDM measurements.