  We discuss some recent attempts to reconcile cosmology with supergravity and
M/string theory. First of all, we point out that in extended supergravities the
scalar masses are quantized in terms of the cosmological constant in de Sitter
vacua: the eigenvalues of the Casimir operator 3 m^2/\Lambda take integer
values. For the current value of the cosmological constant extended
supergravities predict ultra light scalars with the mass of the order of Hubble
constant, 10^{-33} eV. This may have interesting consequences for cosmology.
Turning our attention to cosmological implications of M/string theory, we
present a possibility to use string theory D-brane constructions to reproduce
the main features of hybrid inflation. We stress an important role played by
Fayet-Iliopoulos terms responsible for the positive contribution to the
potentials and stabilization of moduli.
