Title: A New Analytic Approach to Cosmological Perturbations with Applications to Dark Matter Physics and the Early Universe
Since the pathfinding work of Zel’dovich, Peebles and other cosmological pioneers precisely predicting the evolution of the phase-space distribution functions of photons, neutrinos, and other standard model particles
in an expanding big bang cosmology has been both a labour and pastime of theoretical cosmologists. Solving for these distribution functions within linear general relativity is a framework known as cosmological perturbation theory. In the half-century since it’s development it has become increasingly clear that new dark matter particles that respond gravitationally, don’t often interact with standard model particles, but otherwise have unknown interaction properties must also be included. In particular dark matter is required to account for the scale-dependent photon phase-space distribution first precisely measured by WMAP. Over the past two decades numerical codes have been developed that precisely solve linear perturbation theory within the standard cosmological model, but extending these codes to account for the unknown physics of the dark matter or other new phenomena requires significant model-dependent effort. I discuss an analytic approach to solving the integro-differential equation for metric perturbations in a Universe containing both relativistic collisionless particles (like neutrinos) and a tightly-coupled radiative plasma (like photons). Using this method a new family of closed-form solutions to cosmological perturbation theory has been found. These solutions can be employed to quickly determine the matter power spectrum of dark-matter in models with complex dark-matter interactions necessary to initialize non-linear cosmological simulations. A second application of these solutions is efficient computation of the spectral distortions to the CMB due to the dissipative effects of non-linear mode coupling.