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Advanced LIGO and Advanced Virgo have recently published the upper limitmeasurement of persistent directional stochastic gravitational wave background(SGWB) based on data from their first and second observing runs (O1 and O2). Inthis paper we investigate whether a correlation exists between this maximallikelihood SGWB map and the electromagnetic tracers of matter structure in theuniverse, such as galaxy number counts. The method we develop will improve thesensitivity of future searches for anisotropy in the SGWB and expand the use ofSGWB anisotropy to probe the formation of structure in the universe. In orderto compute the cross-correlation, we used the spherical harmonic decompositionof SGWB in multiple frequency bands and converted them into pixel-based skymaps in HEALPix basis. For the electromagnetic (EM) part, we use the SloanDigital Sky Survey (SDSS) galaxy catalog and form HEALPix sky maps of galaxynumber counts at the same angular resolution as the SGWB maps. We compute thepixel-based coherence between these SGWB and galaxy count maps. Afterevaluating our results in different SGWB frequency bands and in differentgalaxy redshift bins, we conclude that the coherence between the SGWB andgalaxy number count maps is dominated by the null measurement noise in the SGWBmaps, and therefore not statistically significant. We expect the results ofthis analysis to be significantly improved by using the more sensitive upcomingSGWB measurements based on the third observing run (O3) of Advanced LIGO andAdvanced Virgo.

Searching for Cross-Correlation Between Stochastic Gravitational Wave Background and Galaxy Number Counts