Gauge-invariant post-Newtonian perturbations in symmetric teleparallel gravity

TL;DR

This paper extends the gauge-invariant parameterized post-Newtonian formalism to symmetric teleparallel gravity by developing a new notion of gauge-invariant perturbations for the connection, enabling its application to these theories.

Contribution

It introduces a novel gauge-invariant perturbation framework for the connection in symmetric teleparallel gravity, expanding the PPN formalism's applicability.

Findings

Lowest order terms expressed in terms of PPN potentials

New gauge-invariant variables for the teleparallel connection

Framework compatible with symmetric teleparallel gravity theories

Abstract

We present an extension to the gauge-invariant formulation of the parameterized post-Newtonian (PPN) formalism, which allows its application to symmetric teleparallel gravity theories. In its original formulation, the gauge-invariant PPN formalism makes use of a gauge-invariant perturbative expansion of tensor fields; however, one of the fundamental gravitational field variables in symmetric teleparallel gravity theories is a flat, torsion-free connection, hence not a tensor field. Since connections transform differently from tensor fields under diffeomorphisms, we introduce here an adapted notion of gauge-invariant perturbation variables for the symmetric teleparallel connection, and show how the lowest order terms can be expressed in terms of the common PPN potentials.