Solar System tests in $f(T)$ gravity

TL;DR

This paper examines how $f(T)$ gravity theories perform against classic solar system tests, deriving solutions for perihelion precession, light bending, Shapiro delay, and redshift, and constrains model parameters using observational data.

Contribution

It provides explicit solutions for solar system tests within $f(T)$ gravity and constrains the model parameters based on observational data, extending previous theoretical work.

Findings

Constraints on $oldsymbol{eta}$ for $f(T)$ models with $n=2,3$

Derived solutions for perihelion precession, light bending, Shapiro delay, and redshift in $f(T)$ gravity

Compatibility of $f(T)$ gravity with solar system observations

Abstract

We investigate the four solar system tests of gravity - perihelion precession, light bending, Shapiro time delay, gravitational redshift - in $f(T)$ gravity. In particular, we investigate the solution derived by Ruggiero and Radicella, Phys. Rev. D 91, 104014 (2015), for a nondiagonal vierbein field for a polynomial $f(T) = T + \alpha T^n$, where $\alpha$ is a constant and $|n| \neq 1$. In this paper, we derive the solutions for each test, in which Weinberg's, Bodenner and Will's, Cattani et al. and Rindler and Ishak's methods are applied, Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity (Wiley, New York, 1972); Am. J. Phys. 71 (2003); Phys. Rev. D 87, 047503 (2013); Phys. Rev. D 76, 043006 (2007). We set a constraint on alpha for $n$ = 2, 3 by using data available from literature.