  We consider two non-standard cosmological scenaria according to which the
universe is reheated to a low reheating temperature after the late decay of a
scalar field or is dominated by the kinetic energy of a quintessence field in
the context of a tracking quintessential model. In both cases, we calculate the
relic density of the \emph{Weakly Interacting Massive Particles} (WIMPs) and
show that it can be enhanced with respect to its value in the standard
cosmology. By adjusting the parameters of the low reheating or the
quintessential scenario, the cold dark matter abundance in the universe can
become compatible with large values for the annihilation cross section times
the velocity of the WIMPs. Using these values and assuming that the WIMPs
annihilate predominantly to $e^+e^-$, $\mu^+\mu^-$ or $\tau^+\tau^-$, we
calculate the induced fluxes of $e^\pm$ cosmic rays and fit the current data of
PAMELA and ATIC or Fermi LAT. We achieve rather good fits especially to PAMELA
and Fermi-LAT data in conjunction with a marginal fulfillment of the
restriction arising from cosmic microwave background, provided that the WIMPs
annihilate predominantly to $\mu^+\mu^-$. In both non-standard scenaria the
required transition temperature to the conventional radiation dominated era
turns out to be lower than about $0.7 \GeV$. In the case of the low reheating,
an appreciable non-thermal contribution to the WIMP relic density is also
necessitated.
