  We discuss the relic abundance of asymmetric Dark Matter particles in
modified cosmological scenarios where the Hubble rate is changed with respect
to the standard cosmological scenario. The modified Hubble rate leaves its
imprint on the relic abundance of asymmetric Dark Matter particles if the
asymmetric Dark Matter particles freeze--out in this era. For generality we
parameterize the modification of the Hubble rate and then calculate the relic
abundance of asymmetric Dark Matter particles and anti--particles. We found the
abundances for the Dark Matter particles and anti--particles are enhanced in
the modified cosmological models. The indirect detection signal is possible for
the asymmetric Dark Matter particles due to the increased annihilation rate in
the modified cosmological models. Applying Planck data, we find the constraints
on the parameters of the modified cosmological models.
