Interplay between Generation Mechanisms and Detection of Supersymmetric Dark Matter in the LHC Era

The object of this thesis is the study of several, possibly complementary, aspects of generation mechanism and detection of the two dark matter (DM) candidates provided by the Minimal Supersymmetric extension of the Standard Model (MSSM), i.e. the gravitino and the neutralino. We have first of all focused on the generation mechanism of neutralino dark matter, examining the possible consequences of relaxing some of the hypothesis on which the typically adopted thermal WIMP paradigm relies. We have, indeed, considered non-thermal dark matter production scenarios motivated, in the context of Supersymmetric theories, in supergravity and superstring frameworks. These classes of theories often feature the presence of long-lived states capable of dominating the energy budget of the Universe at early stages before possibly decaying into dark matter particles. Non thermal production have been studied in a systematic way by mean of a numerical code developed for this purpose. In particular the impact in selecting a preferred mass scale for the Dark matter and, consequently, the impact on the interpretation of new physics discovered or excluded at LHC have been discussed. The second aspect of neutralino dark matter generation which has been investigated is the assumption of kinetic equilibrium during the whole phase of dark matter generation and the validity of the factorization usually implemented to rewrite the system of coupled Boltzmann equation for each coannihilating species as a single equation for the sum of all the number densities. To this purpose has been developed and numerically implemented a formalism for the computation of the kinetic decoupling temperature in the case of coannhilating particles. This formalism has been applied to a definite scenario referred as G2-MSSM. The next topic discussed in this thesis, remaining in the context of neutralino DM, is the capability of current and next generation direct detection experiments of probing the MSSM parameter space. Focusing on some definite setups, satisfying the cosmological bounds on the DM relic density and the current particle physics constraints, the possibility for them of producing direct detection signals has been inspected through Montecarlo Simulations. The final purpose of this analysis is to show as indications about the DM properties, as provided by an experimental detection, can influence some features of the underlying Supersymmetric model which can be probed in the next future by LHC. We have finally moved the focus to the other dark matter candidate within the MSSM, i.e. the gravitino. Remarkably it is a viable dark matter candidate also in presence of R-parity violation. Gravitino dark matter have been studied in the context of a class of Supersymmetric models referred as Tree-Level Gauge Mediation (TGM). These models provide rather definite predictions for the mass of the dark matter being it related to the mechanism of mediation of SUSY breaking. In particular has been investigated a realization of TGM predicting a gravitino mass in the range 10-100 GeV. Cosmological bounds have been investigated both in presence and in absence of R-parity. The model results disfavored in case the R-parity holds, being in severe tension with Big Bang Nucleosynthesis; on the contrary is naturally feasible in presence of a small amount of R-parity violation.