Log-periodic gravitational-wave background beyond Einstein gravity

TL;DR

This paper explores how log-periodic oscillations in the gravitational-wave background can serve as signatures of physics beyond Einstein gravity, with potential detectability in future gravitational-wave observatories.

Contribution

It demonstrates that log oscillations produce a unique spectral shape independent of their origin and can arise in theories beyond Einstein gravity with discrete scale invariance.

Findings

Spectral shape of stochastic background has a unique parametrization.

Log oscillations can be generated in inflationary models beyond Einstein gravity.

Next-generation detectors can detect these features with high SNR.

Abstract

Periodic patterns of logarithmic oscillations can arise in primordial curvature perturbation spectra and in the associated gravitational-wave background via different mechanisms. We show that, in the presence of log oscillations, the spectral shape of the stochastic background has a unique parametrization independent of its physical origin. We also show that this log-periodic modulation can be generated in any scenario beyond Einstein gravity endowed with an approximate discrete scale invariance, a symmetry typical of deterministic fractal spacetimes that could emerge in quantum gravity under certain conditions. We discuss how a log-oscillatory spectral shape arises from concrete inflationary models beyond Einstein gravity and the prospects for detection in Einstein Telescope and other next-generation gravitational-wave observatories. We find that these instruments will be sensitive to log-periodic features if the detection is made with a high signal-to-noise ratio (SNR) and that the error scales as $1/{\rm SNR}$.