Cross-Correlation Analysis of Anisotropic Stochastic Gravitational Wave Background with Electromagnetic Tracers and Methods in Dealing with the Inverse Fisher Matrix

To date, only upper limits for the anisotropic stochastic gravitational wave background (SGWB) have been reported. The cross-correlation of the anisotropic SGWB with different electromagnetic tracers (such as galaxy counts or weak lensing) has the potential to aid in detecting the anisotropic SGWB sooner than directly detecting it. However, an issue in performing the cross-correlation analysis is removing the detector response from the observed gravitational wave data, which implies inversion of an ill-defined Fisher matrix. Past studies have approached the problem by regularizing the Fisher matrix. This approach has been proven successful in studies with relatively low angular resolution. I am working on an alternative method that avoids inversion of the Fisher matrix, hence avoiding placing limitations on the angular resolution of the analysis.