  We review the calculation of the LSP relic density in alternative
cosmological scenarios where contributions from direct decay production are
important. We study supersymmetric models with intermediate unification scale.
We find concrete scenarios where the reheating temperature is of order one GeV
($M_I\sim 10^{12}$) and below. If the case that this reheating temperature is
associated to the decay of oscillating moduli fields appearing in string
theories, we show that the LSP relic density considerably increases with
respect to the standard radiation-dominated case by the effect of the direct
non-thermal production by the modulus field. The LSP can become a good dark
matter candidate ($0.01-0.1 \gsim \Omega h^2 \lsim 0.3-1$) for $M_I\sim
10^{12}-10^{14}$ Gev and $m_\phi\sim 1-10$ TeV.
