Astrophysical Gravitational Wave Backgrounds are not "normal…"

Gravitational wave detectors across the frequency spectrum are expected to observe astrophysical gravitational wave backgrounds (GWBs) that are generated by a finite population of ultra-compact objects such as supermassive black hole binaries. In data analyses, we model the GWB as being "Gaussian," which means that it can be described by a power spectral density (PSD). In this talk, I will give a pedagogical explanation as to why this model is technically incorrect, and discuss why we make this assumption by demonstrating the connection between cosmic variance of a finite population of sources to the PSD of a Gaussian GWB. I will also show how this mismodelling can bias GWB parameter estimation, and what is required to resolve these issues.