Toward a test of Gaussianity of a gravitational wave background

TL;DR

This paper investigates the Gaussianity of a gravitational wave background using pulsar timing array data, finding that two-point statistics may effectively constrain Gaussianity, unlike one-point statistics which are hindered by pulsar noise.

Contribution

It introduces a novel analysis of Gaussianity signatures in gravitational wave backgrounds through cumulants of one- and two-point functions in PTA data, highlighting the potential of two-point statistics.

Findings

One-point statistics are impractical for Gaussianity constraints due to pulsar noise.

Two-point statistics show promise for constraining Gaussianity in PTA data.

Gaussian signatures are applicable to any gravitational wave background.

Abstract

The degree of Gaussianity of a field offers insights into its cosmological nature, and its statistical properties serve as indicators of its Gaussianity. In this work, we examine the signatures of Gaussianity in a gravitational wave background (GWB) by analyzing the cumulants of the one- and two-point functions of the relevant observable, using pulsar timing array (PTA) simulations as a proof-of-principle. This appeals to the ongoing debate about the source of the spatially-correlated common-spectrum process observed in PTAs, which is likely associated with a nanohertz stochastic GWB. We investigate the distribution of the sample statistics of the one-point function in the presence of a Gaussian GWB. Our results indicate that, within PTAs, one-point statistics are impractical for constraining the Gaussianity of the nanohertz GWB due to dominant pulsar noises. However, our analysis of two-point statistics shows promise, suggesting that it may be possible to constrain the Gaussianity of the nanohertz GWB using PTA data. We also emphasize that the Gaussian signatures identified in the one- and two-point functions in this work are expected to be applicable to any gravitational wave background.