© 2015 Dr. Vikram RaviSupermassive black holes (SMBHs) are inferred to exist at the centres of massive galaxies throughout the Universe. When two such galaxies merge, a binary SMBH system is likely to form, which coalesces following losses of energy and angular momentum to gravitational waves (GWs). GWs from binary SMBHs will cause metric perturbations at the Earth that affect the arrival times of pulses from radio pulsars within our Galaxy. This concept has led to the establishment of pulsar timing array (PTA) collaborations, which are primarily aimed at detecting GWs. This thesis is motivated by the prospect of gleaning insights into the assembly histories of the cosmological SMBH and galaxy populations by searching for GWs from binary SMBHs. I show that a GW background (GWB) generated by the binary SMBH population is the most promising class of signal to consider for this purpose, with the strong possibility of a detection within the forthcoming decade. In contrast, I find that GWs from individual binary SMBHs are not viable sources for current PTA searches. I also demonstrate that the statistics of pulsar timing variations induced by the GWB will be mildly non-Gaussian. By developing techniques to simulate the effects of GWs from predicted populations of binary SMBHs on PTA data, I find that these non-Gaussian statistics result in a ∼ 10% degradation in the recent Parkes PTA upper limit on the GWB. In a separate investigation, I show that interactions between binary SMBHs and their environments may cause attenuation in the GWB at frequencies up to 10^−8 Hz. Finally, upon comparing various predictions for the GWB with the most recent upper limits from the Parkes PTA, I find that a model which posits purely merger-driven growth of massive galaxies during the last 8 billion years is excluded at the 91% confidence level. I also derive a constraint on the merger timescale of massive galaxies: I find that the mean time spent between projected separations of 20 and 5 h^−1 kpc is greater than 0.1 Gyr with 95% confidence
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