The stochastic gravitational wave background (SGWB) contains a wealth of information on astrophysical and cosmological processes. A major challenge of upcoming years will be to extract the information contained in this background and to disentangle the contributions of different sources. In this paper we provide the formalism to extract, from the correlation of three signals in the Laser Interferometer Space Antenna (LISA), information about the tensor three-point function, which characterizes the non-Gaussian properties of the SGWB . This observable can be crucial to discriminate whether a SGWB has a primordial or astrophysical origin. Compared to the two-point function, the SGWB three-point function has a richer dependence on the gravitational wave momenta and chiralities. It can be used therefore as a powerful discriminator between different models. For the first time we provide the response functions of LISA to a general SGWB three-point function. As examples, we study in full detail the cases of an equilateral and squeezed SGWB bispectra, and provide the explicit form of the response functions, ready to be convoluted with any theoretical prediction of the bispectrum to obtain the observable signal. We further derive the optimal estimator to compute the signal-to-noise ratio. Our formalism covers general shapes of non-Gaussianity, and can be extended straightaway to other detector geometries. Finally, we provide a short overview of models of the early universe that can give rise to a non-Gaussian SGWB.
Bibliographical noteFunding Information:
We thank Raphael Flauger, Michele Liguori, Sabino Matarrese, and Germano Nardini for useful discussions. We thank the Mainz Institute for Theoretical Physics (MITP) for hosting the IV LISA workshop, where this work has started. N.B acknowledges partial financial support by ASI Grant No. 2016-24-H.0. The work of D.G.F was supported by the Swiss National Science Foundation. J.G-B thanks the Theory Department at CERN for their hospitality during his sabbatical year at CERN. His work is supported by the Research Project FPA2015-68048-C3-3-P (MINECO-FEDER), the Centro de Excelencia Severo Ochoa Program SEV-2016-0597, and the Salvador de Madariaga Program ref. PRX17/00056. The work of M. Pe was supported in part by the DOE grant de-sc0011842 at the University of Minnesota. M. Pi acknowledges the support of the Spanish MINECO’s Centro de Excelencia Severo Ochoa Program SEV-2016-0597. This project has received funding from the European Unions Horizon 2020 research and innovation programme under the Marie Sk lodowska-Curie grant agreement No 713366. The work of M.S is supported in part by the Science and Technology Facility Council (STFC), U.K., under the research grant ST/P000258/1. The work of L.S is partially supported by the US-NSF grant PHY-1520292. G.T is partially funded by the STFC grant ST/P00055X/1.
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