As the largest gravitationally bound objects in the Universe, galaxy clusters can be used to probe a variety of topics in astrophysics and cosmology. This thesis describes the development of an algorithm to find galaxy clusters using non-parameteric methods applied to catalogs of galaxies generated from multi-colour CCD observations. It is motivated by the emergence of increasingly large, photometric galaxy surveys and the measurement of key cosmological parameters through the evolution of the cluster mass function. The algorithm presented herein is a reconstruction of the successful, spectroscopic cluster finding algorithm, C4 (Miller et al., 2005), and adapting it to large photometric surveys with the goal of applying it to data from the Dark Energy Survey (DES). AperC4 uses statistical techniques to identify collections of galaxies that are unusually clustered in a multi-dimensional space. To characterize the new algorithm, it is tested with simulations produced by the DES Collaboration and I evaluate its application to photometric datasets. In doing so, I show how AperC4 functions as a cosmology independent cluster finder and formulate metrics for a \successful" cluster finder. Finally, I produce a galaxy catalog appropriate for statistical analysis. C4 is applied to the SDSS galaxy catalog and the resulting cluster catalog is presented with some initial analyses.

In this thesis, we present three projects that describe the use of the XMM-Newton Cluster Survey (XCS) to investigate exotic astrophysical phenomena. Each project widens the scope of XCS beyond the study of cluster cosmology. In the first project, we derive correlations between X-ray properties of Active Galactic Nuclei (AGN) and mass of its Super Massive Black Hole (SMBH). These properties are the X-ray luminosity (LX) and a measure of the variability of the AGN - the normalised excess variance (σ2NXS). We confirm previous results indicating an anti-correlation between black hole mass (MBH) and σ2NXS, as well as anti-correlation between LX and σ2NXS, and a positive correlation between LX and MBH. We investigate whether there is a redshift evolution in these relations. We then develop methods to estimate MBH from short exposure X-ray observations specific to the eROSITA observatory, to allow us to measure LX of millions of AGN. The second project describes a new method to detect the rarest of X-ray transient sources, X-ray ashes (XRFs), through a serendipitous search of the XCS catalogue. We categorize the detected XRF candidates and look in more detail at one that is most likely to be an XRF. Based on its properties, we estimate an upper limit to their occurrence. A third project describes our method to search for an unknown emission line in the stacked spectra of galaxy clusters from the XCS extended source catalogue. This line, if found, may be evidence of a hypothetical particle - the sterile neutrino - which has been postulated as a candidate for dark matter. We review other research that has led to published work, as well as laying the foundation for future collaborations. This includes work on improving the XCS temperature pipeline in order to estimate the temperatures of galaxy clusters.

The effective theory of gravity coupled to matter represents a fully consistent low energy theory of quantum gravity coupled to the known particles and forces of the standard model. In recent years this framework has been extensively used to make physical predictions of phenomena in high energy physics and cosmology. In this thesis we use theoretical tools and experimental data to place constraints on various popular models which utilise this framework. We speciffically derive unitarity bounds in grand unified theories, models of low scale quantum gravity, models with extra dimensions and models of Higgs inflation. We also derive a bound on the size of the Higgs boson's non-minimal coupling to gravity. This represents an important area of research because it helps us to better understand the theories and models that many physicists are currently working on and crucially it can inform us where we can reliably use the effective theory approach and where it breaks down.