Primordial observables of explicit diffeomorphism violation in gravity

TL;DR

This paper explores how explicit diffeomorphism violation in gravity could leave detectable imprints on primordial gravitational waves, with predictions for observables and constraints from current and future detectors.

Contribution

It derives the effects of symmetry breaking on primordial gravitational wave spectra and assesses the observability limits with various gravitational-wave detectors.

Findings

aLIGO could detect violations with s_{00}   -0.1

LISA and DECIGO could probe violations as small as 5 10^{-4} and 3 10^{-3}

Constraints from  N_{ m eff} are consistent with bounds from gravitational wave speed

Abstract

We investigate the potential for current and future gravitational-wave detectors to observe imprints of explicit diffeomorphism violation in primordial signals. Starting from a simple model with known effects, we derive the strain amplitude and power spectrum for primordial gravitational waves, both of which are affected by the symmetry breaking. Through this, we directly find predictions for the tensor spectral index and tensor-to-scalar which are different from general relativity. By considering the known sensitivity curves for NANOGrav, SKA, THEIA, $\mu$-ARES, ASTROD-GW, LISA, BBO, DECIGO, CE, AION-km, AEDGE, ET, and aLIGO, we place observability limits on the parameters controlling the diffeomorphism violation. For instance, we find that aLIGO could observe signals for \(s_{00} \lesssim -0.1\), while more sensitive future detectors like LISA and DECIGO could probe violations as small as \(s_{00} \approx -5 \times 10^{-4}\) and \(-3 \times 10^{-3}\), respectively. Finally, we consider the existing constraints on the number of relativistic degrees of freedom $\Delta N_{\rm eff}$ which is tightly constrained by Big-Bang Nucleosynthesis (BBN) and we find that $\Delta N_{\rm eff}$ only weakly depends on the symmetry breaking but places a lower bound on the coefficients which is consistent with available bounds from the speed of gravitational waves.