The next generation of large-scale galaxy surveys, across the electromagnetic spectrum, loom on the horizon as explosively game-changing datasets, in terms of our understand- ing of cosmology and structure formation. We are on the brink of a torrent of data that is set to both confirm and constrain current theories to an unprecedented level, and potentially overturn many of our conceptions. One of the great challenges of this forthcoming deluge is to extract maximal scientific content from the vast array of raw data. This challenge requires not only well- understood and robust physical models, but a commensurate network of software implementations with which to efficiently apply them. The halo model, a semi-analytic treatment of cosmological spatial statistics down to nonlinear scales, provides an excellent mathematical framework for exploring the nature of dark matter. This thesis presents a next-generation toolkit based on the halo model formalism, intended to fulfil the requirements of next-generation surveys. Our toolkit comprises three tools: (i) hmf, a comprehensive and flexible calculator for halo mass functions (HMFs) within extended Press-Schechter theory, (ii) the MRP distribution for extremely efficient analytic characterisation of HMFs, and (iii) halomod, an extension of hmf which provides support for the full range of halo model components. In addition to the development and technical presentation of these tools, we apply each to the task of physical modelling. With hmf, we determine the precision of our knowledge of the HMF, due to uncertainty in our knowledge of the cosmological parameters, over the past decade of cosmic microwave background (CMB) experiments. We place rule-of-thumb uncertainties on the predicted HMF for the Planck cosmology, and find that current limits on the precision are driven by modelling uncertainties rather than those from cosmological parameters. With the MRP, we create and test a method for robustly fitting the HMF to observed masses with arbitrary measurement uncertainties on a per-object basis. We find that our method reduces estimation uncertainty on parameters by over 50%, and correctly accounts for Eddington bias even in extremely poorly measured data. Additionally, we use the analytical properties of the MRP to obtain asymptotically correct forms for the stellar-mass halo-mass relation, in the subhalo abundance matching scheme. Finally, with halomod, we explore the viability of the halo model as a test of warm dark matter (WDM) via galaxy clustering. Examining three distinct scale regimes, we find that the clustering of galaxies at the smallest resolvable scales may provide a valuable independent probe in the coming era.

{"references": ["Abazajian, K. N. (2006). Phys. Rev. D 73.6, p. 063513.; Allen, S. W., A. E. Evrard, and A. B. Mantz (2011). Annu. Rev. Astron. Astrophys. 49.1, pp. 409\u2013470."]}

226 Pages (248 incl. Front Matter)