Searching for bispectrum of stochastic gravitational waves with pulsar timing arrays

Abstract

We study how to probe bispectra of stochastic gravitational waves with pulsar timing arrays. The bispectrum is a key to probe the origin of stochastic gravitational waves. In particular, the shape of the bispectrum carries valuable information of inflation models. We show that an appropriate filter function for three point correlations enables us to extract a specific configuration of momentum triangles in bispectra. We also calculate the overlap reduction functions and discuss strategy for detecting the bispectrum with multiple pulsars.

Probing a stationary non-Gaussian background of stochastic gravitational waves with pulsar timing arrays

“…We now analyze the 3-point overlap function for flattend tensor bispectra satisfying a stationarity condition, as described in Section 2. Such shapes of tensor bispectra were not specifically investigated in [29], hence our results are new. In correlating signals from different pulsars, we assume that the frequencies of the GWs are comparable, hence the flattened tensor bispectra in momentum space have a shape with sides of similar size, see the right panel of Fig 1. The tensor 3-point function in Fourier space is given by eq (15).…”

“…For definiteness, here we focus our attention on a system where the three pulsars lie on orthogonal planes, (x, y), (x, z), (y, z): see In this case, the 3-point overlap function depends on two angles ζ and χ between the vectors from earth towards the pulsars. We represent our results for the overlap functions in Fig 8, evaluated using the general formula (29). Also in this case the typical magnitude of the overlap function is of order of a few percent.…”

“…Reviews can be found in [2,27,28]. See also [29] for a study of overlap functions for 3-point non-Gaussian correlators with PTA (we will discuss in footnote 6 the differences between [29] and our work). Discussions on tests of deviations from General Relativity with PTAs can be found e.g.…”

Modern Topics in Scalar Field Cosmology

“…We express the graviton mode in real space as Following the review in [243], we define the total time-delay output s α measured by a GW experiment based on a PTA system as sum of a GW signal σ α , and the noise n a . We assume that the noise is uncorrelated with 6 An interesting study of PTA 3-point overlap functions, with the aim of to investigate tensor non-Gaussianity, has been carried on in [264]. But that work did not specifically analyzed flattened triangular shapes, that as we learned are the physically relevant ones in the context of stationary non-Gaussianity.…”

“…Reviews can be found in [243,262,263]. See also [264] for a study of overlap functions for 3-point non-Gaussian correlators with PTA (we will discuss in footnote 6 the differences between [264] and our work).…”