Parametrized post-Newtonian formalism in higher-order Teleparallel Gravity

TL;DR

This paper investigates the post-Newtonian limit of higher-derivative Teleparallel Gravity, showing it aligns with General Relativity at the PPN level but highlighting the potential for new observable effects at higher orders.

Contribution

It extends previous PPN analyses to higher-order Teleparallel Gravity, emphasizing the importance of second-order and cosmological perturbations for detecting deviations.

Findings

Higher-order Teleparallel Gravity is fully conservative and indistinguishable from GR at PPN level.

Second post-Newtonian order or PPNC framework may reveal new observable signatures.

The study emphasizes the need for higher-order analysis to detect modifications in Teleparallel Gravity.

Abstract

We study the parametrized post-Newtonian (PPN) limit of higher-derivative-torsion Modified Teleparallel Gravity. We start from the covariant formulation of modified Teleparallel Gravity by restoring the spin connection of the theory. Then, we perform the post-Newtonian expansion of the tetrad field around the Minkowski background and find the perturbed field equations. We compute the PPN metric for the higher-order Teleparallel Gravity theories which allows us to show that at the post-Newtonian limit this more general class of theories are fully conservative and indistinguishable from General Relativity . In this way, we extend the results that were already found for $F(T)$ gravity in previous works. Furthermore, our calculations reveal the importance of considering a second post-Newtonian (2PN) order approximation or a parametrized post-Newtonian cosmology (PPNC) framework where additional perturbative modes coming from general modifications of Teleparallel Gravity could lead to new observable imprints.