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The understanding of the nature of the dominant forms of matter and energy in the Universe is undoubtedly one of the most intriguing concepts within the vast domain of current scientific research. Current experimental evidence supports the notion that the dominant form of matter in the Universe is composed of a non-luminous, possibly exotic, material that is distinct from the familiar baryonic matter from which the luminous Universe is composed.

In this thesis we present some phenomenological investigations of freeze-in models of dark matter and also a numerical calculation of the particle flux produced by dark matter annihilations around a rotating black hole. Freeze-in is an alternative dark matter production mechanism in which an out of equilibrium very weakly coupled particle is produced in the early universe. We consider the Minimal Supersymmetric Standard Model (MSSM) extended by an additional singlet superfield feebly coupled to the other particles. This feeble coupling leads to a long lifetime for the next to lightest superpartner which can only decay via this coupling. The long lifetime of this decaying particles could lead to displaced vertices which provide a prominent signal for beyond the standard model physics. The phenomenology of the signals from this simple Feebly Interacting Massive Particle (AMP) model is investigated and compared to some experimental searches. The freeze-in mechanism may also constitute an alternative for generating the correct relic density for dark matter candidates whose predicted freeze-out abundance is too low due to a large total annihilation cross section. We show that although such a mechanism could explain why a dark matter candidate has the correct relic density, some candidates may still be ruled out because they would lead to a large gamma ray flux in dwarf spheroidal galaxies or a large elastic scattering rate in direct detection experiments. To investigate this scenario we examine neutralino dark matter in the MSSM. Collisions around black holes may provide a window onto very high energy physics. The geodesics of massless particles produced in collisions near a rotating black hole are solved numerically and a Monte Carlo integration of the momentum distribution of the massless particles is performed to calculate the fraction that escape the black hole to infinity. A distribution of in falling dark matter particles, which are assumed to annihilate to massless panicles, is considered and an estimate of the emergent flux from the collisions is made. The energy spectrum of the emergent particles is found to contain two Lorentz shifted peaks centred on the mass of the dark matter. The separation of the peaks is found to depend on the density profile of the dark matter and could provide information about the size of the annihilation plateau around a black hole and the mass of the dark matter particle.

The quenching factor for sodium recoils in a 2-inch Nal(Tl) scintillating crystal has been measured at room temperature. The crystal has been exposed to 2.45 MeV monoenergetic neutrons generated by a deuterium-deuterium fixed target accelerator in the energy range 10 to 100 keV nuclear recoil energy. A BC501A liquid scintillator detector has been used to tag neutrons that scatter off sodium nuclei in the crystal. Cuts on pulse shape discrimination in BC501A and neutron time of flight have been performed on pulses recorded by an Acqiris DC265 digitiser with a 2 ns sampling time. A quenching factor of 25.2 ± 6.4% has been determined for 10 keV sodium recoils. Measured quenching factors range from 19% to 26% in good agreement with other experiments. From pulse shape analysis, the mean time of pulses from electron and nuclear recoils have been compared down to 2 keV electron equivalent energy.