Post-Newtonian Approximation of Teleparallel Gravity Coupled with a Scalar Field

TL;DR

This paper investigates the weak field limit of a teleparallel gravity theory coupled with a scalar field using PPN formalism, finding it aligns with general relativity in Solar System tests, unlike scalar-tensor theories.

Contribution

It demonstrates that teleparallel gravity with a scalar field has PPN parameters identical to GR, offering a viable alternative compatible with Solar System experiments.

Findings

PPN parameters match those of GR

Theory passes Solar System experimental constraints

Differs from scalar-tensor theories in parameter constraints

Abstract

We use the parameterized post-Newtonian (PPN) formalism to explore the weak field approximation of teleparallel gravity non-minimally coupling to a scalar field $\phi$, with arbitrary coupling function $\omega(\phi)$ and potential $V(\phi)$. We find that all the PPN parameters are identical to general relativity (GR), which makes this class of theories compatible with the Solar System experiments. This feature also makes the theories quite different from the scalar-tensor theories, which might be subject to stringent constraints on the parameter space, or need some screening mechanisms to pass the Solar System experimental constraints.