Application of cosmic microwave background techniques to a gravitational wave stochastic background

Abstract

The detection of gravitational waves by the LIGO and Virgo collaborations has allowed us to view the universe in new way and given us direct measurements of black holes for the first time. In coming years we will be able to measure not only individual burst sources but also the stochastic background of gravitational waves permeating the universe. This will be a treasure trove of information about the universe, from which we will be able to learn about a vast range of areas including astrophysics (such as that of compact binaries), cosmology of cosmic strings and inflation and even the nuclear physics involved in neutron stars. This is particularly exciting because of what we have already been able to measure from the observations we have, such as putting constraints on the Hubble constant. It will, however, lead to new challenges, in particular how best to analyse the background. The purpose of this thesis is to use analogies to the cosmic microwave background angular power spectra in order to generate and compare two different formalisms for this analysis — one based upon the amplitude signals and one on the gravitational wave Stokes parameter. I will show their respective strengths and weaknesses in analysing the forthcoming data and, specifically, we will see that the Stokes parameters calculations are able convey information about anisotropic and correlated signals that the amplitudes cannot. I will also consider how well we will be able to measure a given background by studying the sensitivity of different detectors to these different formalisms, showing that a detector in motion has many advantages over one that is effectively stationary. Finally, I apply these techniques to showing that we can use multiple independent measurements to recover the angular power spectra for a given background.