Gravitational lensing of gravitational waves

Gravitational Waves have opened an entirely new window into the universe, allowing for the probing of non-luminous matter. Dark Matter has thus far been an extremely difficult subject to study given that until now, it has been very difficult to directly investigate. Gravitational waves allow for solutions to this - one of these is by examining the phenomenon of Gravitational Lensing. The lensing of Gravitational Waves is marked by one of several profiles dependent upon the mass-density profile of the object that has done the lensing. It is this that allows for the probing of Dark Matter should it be the case that when detected, it is possible to determine if a signal is lensed and if so, by what profile. Thus it is urgently necessary to investigate the detectability of a lensed signal and to examine the possibility of determining which type a signal is. In this work, a piece of software was developed in the python programming language using the work of Antonio Hererra Martin who created individual scripts to generate the amplification factors for each of the lensing types considered, and a tool called `bilby' designed to perform nested sampling and to present the many gravitational wave specific tools of the LIGO Algorithm Library Suite (LALSuite) to calculate Bayes Factors comparing each of the models with each of the other models, presenting a quantitative analysis of the ability to distinguish signal types. This software was initially tested by comparison of those lens profiles that were able to be fully integrated, and proof that those more complex could not be integrated further, comparison between bilby generated evidence and the evidence analytically calculated for a simple toy problem, and by comparison of lensed and unlensed signal types using a Fitting Factor developed, first analysed in the Cao et. al (2014) paper. Each of these tests were able to justify that the software was in a functional state to be used for its primary task. Performing the main analysis using simulated data yielded that in principle the signals received at detectors are able to be correctly identified as the signal type that they are, however, that this ability is dependent upon the parameters of the lens and the signal itself. There are limits based in, at least, the mass of the lensing object and the distance at which the signal originates from the observatory