  It is generally well known that the Standard Model of particle physics is not
the ultimate theory of fundamental interactions as it has inumerous unsolved
problems, so it must be extended. Deciphering the nature of dark matter remains
one of the great challenges of contemporary physics. Supersymmetry is probably
the most attractive extension of the SM. In the first part of this thesis we
study the interparticle potentials generated by the interactions between
spin-1/2 sources that are mediated by spin-1 particles in the limit of low
momentum transfer. We investigate different representations of spin-1 particle
to see how it modifies the profiles of the interparticle potentials and we also
include in our analysis all types of couplings between fermionic currents and
the mediator boson. The spin- and velocity-dependent interparticle potentials
that we obtain can be used to explain effects possibly associated to new
macroscopic forces such as modifications of the inverse-square law and possible
spin-gravity coupling effects. The second part of this thesis is based on the
dark matter phenomenology of well-motivated $U(1)'$ extensions of the Minimal
Supersymmetric Standard Model. In these models the right-handed sneutrino is a
good DM candidate whose dark matter properties are in agreement with the
present relic density and current experimental limits on the DM-nucleon
scattering cross section. In order to see how heavy can the RH sneutrino be as
a viable thermal dark matter candidate we explore its DM properties in the
parameter region that minimize its relic density via resonance effects and thus
allows it to be a heavier DM particle. We found that the RH sneutrino can
behave as a good DM particle within minimal cosmology even with masses of the
order of tens of TeV, which is much above the masses that viable thermal DM
candidates usually have in most of dark matter particle models.
