Constraining f(T) gravity in the Solar System

TL;DR

This paper investigates how modifications to teleparallel gravity, specifically $f(T)$ models, affect solar system dynamics and uses spacecraft data to constrain model parameters, potentially improving existing bounds significantly.

Contribution

It provides the first weak-field solutions for $f(T)=T+ ext{constant} imes T^n$ in spherical symmetry and applies them to solar system data to constrain the model parameter $eta$.

Findings

Constraints on $eta$ could improve by 1-3 orders of magnitude.

Solar system data can effectively test $f(T)$ gravity models.

Perturbations from GR are detectable with current spacecraft tracking.

Abstract

In the framework of $f(T)$ theories of gravity, we solve the field equations for $f(T)=T+\alpha T^{n}$, in the weak-field approximation and for spherical symmetry spacetime. Since $f(T)=T$ corresponds to Teleparallel Gravity, which is equivalent to General Relativity, the non linearity of the Lagrangian are expected to produce perturbations of the general relativistic solutions, parameterized by $\alpha$. Hence, we use the $f(T)$ solutions to model the gravitational field of the Sun, and exploit data from accurate tracking of spacecrafts orbiting Mercury and Saturn to infer preliminary insights on what could be obtained about the model parameter $\alpha$ and the cosmological constant $\Lambda$. It turns out that improvements of about one-three orders with respect to the present-day constraints in the literature of magnitude seem possible.