  In the present thesis I studied the phenomenology arising from a class of
string models called sequestered compactifications, which were born with the
aim of getting low-energy SUSY from strings. This is not an easy task if
combined with cosmological constraints, since the mechanism of moduli
stabilization fixes both the scale of supersymmetric particles and the scale of
moduli, which tend to be of the same order. However, if on the one hand
supersymmetric particles with TeV mass are desired in order to address the
hierarchy problem, on the other hand the cosmological moduli problem requires
the moduli to be heavier than 100 TeV. The specific setup of sequestered
compactifications makes this hierarchy achievable, at least in principle: as in
these models the visible sector is located on a stack of D3-branes at
singularities, a physical separation between the visible degrees of freedom and
the SUSY-breaking sources takes place. Such decoupling translates into a
hierarchy between the scale of SUSY-breaking and the spectrum of supersymmetric
particles. Moreover, it is interesting to notice that moduli are the
four-dimensional manifestation of the existence of extra-dimensions, and then
their presence is a common feature of all string compactifications. Since they
are gravitationally coupled, they could decay late in the history of the
universe, affecting in a significant way its cosmological evolution. Possible
deviations of the cosmological observables from the values predicted by the
standard Hot Big Bang Theory constitute an interesting alternative for the
discovery of BSM physics, which is complementary to the particle physics
search. For this reason in addition to SUSY-breaking in sequestered models, I
also studied several cosmological scenarios arising from them, such as
production of non-thermal dark matter and dark radiation, reheating from moduli
decay and inflation.
