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Abstract

This thesis is concerned with the investigation of late-time large-scale cosmic structure formation by applying non-perturbative functional methods to a field-theoretic description of dark matter. To account for phenomena beyond the standard perfect fluid approximation, the kinetic theory description of dark matter is extended by including velocity dispersion degrees of freedom. As an effective theory description, this naturally allows to describe the evolution of dark matter after shell-crossing where the perfect fluid approximation breaks down. To probe the non-linear regime of cosmic structure formation where standard perturbative methods fail, the Dyson–Schwinger equation and the functional renormalisation group are employed. These naturally allow for non-perturbative approximation schemes that are necessary to capture the relevant physics at non-linear scales. The functional renormalisation group is used to solve the large wave number sector using Ward identities related to an extended version of Galilean invariance as well as to investigate time-local dynamics for an effective fluid description of dark matter. Moreover, the emergence and evolution of dark matter vorticity and velocity dispersion are studied with the Dyson–Schwinger equation, leading to the non-perturbative prediction of correlations from first principles.