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

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.

💡 Research Summary

This paper investigates how recent detections of a stochastic gravitational‑wave background (SGWB) by pulsar timing arrays (PTAs) constrain symmetric teleparallel f(Q) gravity, a class of modified gravity theories in which the non‑metricity scalar Q replaces curvature or torsion as the source of gravitation. In the simplest phenomenological model the function takes the form f(Q)=α+βQⁿ, where the exponent n encodes deviations from General Relativity (GR): n=1 recovers GR, while n≠1 produces a modified damping of tensor modes during cosmic expansion. The authors assume that gravitational waves travel at the speed of light (c_T=1), consistent with multimessenger constraints from GW170817, and focus on the damping parameter ν = H⁻¹ d ln f_Q/dt, which they parameterise through n.

Starting from the standard inflationary tensor power spectrum P_t(k)=A(k/k_*)^{n_t}, they derive an analytic approximation for the transfer function of tensor perturbations in f(Q) gravity: T_MG(k,η)=exp