Compact stars in $f(T) = T +ξT^β$ gravity

Abstract: The Teleparallel Theory is equivalent to General Relativity, but whereas in the latter gravity has to do with curvature, in the former gravity is described by torsion. As is well known, there is in the literature a host of alternative theories of gravity, among them the so called extended theories, in which additional terms are added to the action, such as for example in the $f(R)$ and $f(T)$ gravities, where $R$ is the Ricci scalar and $T$ is the scalar torsion, respectively. One of the ways to probe alternative gravity is via compact objects. In fact, there is in the literature a series of papers on compact objects in $f(R)$ and $f(T)$ gravity. In particular, there are several papers that consider $f(T) = T + \xi T^2$, where $\xi$ is a real constant. In this paper, we generalise such extension considering compact stars in $f (T ) = T + \xi T^\beta$ gravity, where $\xi$ and $\beta$ are real constants and looking out for the implications in their maximum masses and compactness in comparison to the General Relativity. Also, we are led to constrain the $\beta$ parameter to positive integers which is a restriction not imposed by cosmology.