Cosmological models within $f(T,B)$ gravity in a holographic framework

We investigate the cosmological evolution of the universe for a spatially flat FLRW background space within the context of $f(T,B)$ gravity, which is a recently formulated teleparallel theory that connects both $f(T)$ and $f(R)$ gravity under suitable limits. The analysis has been done by focusing on four different $f(T,B)$ cosmological models corresponding to various choices of scale factor, namely emergent, logamediate, and intermediate. In addition to this, we also assume a power-law-like function of $f(T,B)$ gravity. The reconstruction of $f(T,B)$ gravity has been done by considering the Holographic Ricci Dark Energy(HRDE) (a particular case of a highly generalized holographic dark energy given in Nojiri et al. in General Relativity and Gravitation, 38, pp.1285-1304,2006) as the background fluid. We analyze the equation of state parameters and the squared speed of sound for the reconstructed models. Finally, we conducted the thermodynamical analysis for each reconstructed model. The generalised second law of thermodynamics(GSLT) is valid for the four different $f(T,B)$ cosmological models.