Prospective bounds on f(Q) gravity with pulsar timing arrays

TL;DR

This paper investigates how pulsar timing arrays can constrain $f(Q)$ gravity, a theory modifying General Relativity through non-metricity, by analyzing gravitational wave damping and forecasting future observational improvements.

Contribution

It provides a model-independent analysis of gravitational wave damping in $f(Q)$ gravity and forecasts SKA's potential to distinguish it from GR.

Findings

Current data are consistent with GR but allow small deviations.

An analytic approximation for the tensor mode transfer function is derived.

Future SKA observations could significantly tighten constraints on $f(Q)$ gravity.

Abstract

Pulsar timing arrays (PTAs) have recently provided compelling evidence for a stochastic gravitational wave background (SGWB) in the nanohertz frequency band, offering a unique window into fundamental physics. Here, we explore implications for symmetric teleparallel $f(Q)$ gravity, a theory in which deviations from General Relativity (GR) arise through the non-metricity scalar $f(Q)$. Crucially, tensor modes propagate at the speed of light in this framework. However, their amplitude undergoes a modified damping during their evolution. We adopt a model-independent parameterization and derive an analytic approximation to the tensor mode transfer function to obtain the spectral energy density of primordial inflationary gravitational waves. Comparison with the NANOGrav 15-year and IPTA second data releases show that the inferred damping parameter $n$ remains consistent with GR, yet allows small deviations that could be observable. We then conduct a Fisher information matrix forecasts which demonstrate that the Square Kilometre Array (SKA) observatory will improve these constraints by several orders of magnitude, offering the potential to distinguish $f(Q)$ gravity from GR with high precision. These results highlight PTAs as powerful probes of non-metricity-based modifications to gravity.