Constraining $f(T,B)$ teleparallel gravity from energy conditions

$f(T,B)$ teleparallel gravity is a recently proposed straightforward generalization of the popular $f(T)$ teleparallel gravity by the incorporation of a boundary term $B=\frac{2}{e}\partial_{i}(e T ^{i}) = \bigtriangledown_{i}T^{i}$ where $T$ denote the torsion scalar \cite{ftb13}. In this work, I investigate the viability of some well motivated $f(T,B)$ teleparallel gravity models of the forms $f=αB^n+βT^m$, $f=αB^n T^m$ and $f=α\log (B)+βT$ where $α, β, n$ and $m$ are free parameters from the inequalities imposed the the weak energy condition. I use the recent estimates of Hubble, deceleration, jerk and snap parameters in finding corners in parameter spaces for the cosmological models for which the energy density remain positive and the weak energy condition ( i.e, $ρ+p \geq 0$, where $p$ and $ρ$ represent respectively the cosmological pressure and energy density) attains a minute positive value, as this implies the EoS parameter $ω= p/ρ\simeq-1$ and therefore consistent with an accelerating universe.

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