Novel Theories Of Dark Matter

The primary aim of this thesis is to explore new theories of dark matter (DM) that reproduce the MOdified Newtonian Dynamics (MOND) phenomenology on galactic scales while preserving the success of the standard Lambda-Cold Dark Matter model on cosmological scales. We begin with a brief survey of the DM problem and note the various challenges posed to Cold Dark Matter (CDM) on small, galactic scales, especially the empirical scaling relations for disk galaxies. We then study the theory of superfluid DM to see how it can provide a solution to these small-scale challenges. The superfluid phonons are described by a MOND-like Lagrangian and mediate a MONDian acceleration between baryons. We then derive the finite-temperature equation of state of DM superfluids with 2-body and 3-body contact interactions. The calculation uses a self-consistent mean-field approximation and relies on the Hartree-Fock-Bogoliubov approximation. Crucially, our approach uses the recent Yukalov-Yukalova proposal of using two chemical potentials to circumvent the well-known Hohenberg-Martin dilemma. Next we propose a theory of DM in which the MOND empirical law is the result of short-ranged interactions between baryons and ‘Baryon-Interacting Dark Matter’(BIDM), which heat up the DM. Following a bottom-up, hydrodynamical approach, we find that the MOND empirical law follows if: i) the BIDM equation of state approximates that of an ideal gas ii) the BIDM relaxation time is order the Jeans time; iii) the heating rate is inversely proportional to the BIDM density. Subsequently we revisit the problem of describing a BEC through a scalar field exhibiting spontaneous symmetry breaking. We perform a self-consistent relativistic calculation using the techniques of thermal field theory to resolve this problem in the two chemical potential framework. Finally, we work out the effective field theory description of a superfluid at temperatures close to zero, starting from the microphysics of a Bose gas having n-body contact interactions.