Effective Search Templates for a Primordial Stochastic Gravitational Wave Background

TL;DR

This paper investigates the detection of a primordial stochastic gravitational-wave background with a sharp spectral feature, showing that simple templates are effective even when the spectrum has complex features.

Contribution

It demonstrates that simple power-law templates are sufficient for detecting complex spectral features in the stochastic gravitational-wave background.

Findings

SNR is maximized with the correct spectral template.

Sensitivity to template shape is weak, favoring simple templates.

Detection remains feasible despite spectral complexities.

Abstract

We calculate the signal-to-noise ratio (SNR) of the stochastic gravitational-wave background in an extreme case that its spectrum has a sharp falloff with its amplitude close to the detection threshold. Such a spectral feature is a characteristic imprint of the change in the number of relativistic degrees of freedom on the stochastic background generated during inflation in the early Universe. We find that, although SNR is maximal with the correct template which is proportional to the assumed real spectrum, its sensitivity to the shape of template is fairly weak indicating that a simple power-law template is sufficient to detect the signature.