  Asymmetric dark matter (ADM) is an attractive framework relating the observed
baryon asymmetry of the Universe to the dark matter density. A composite
particle in a new strong dynamics is a promising candidate for ADM as the
strong dynamics naturally explains the ADM mass in the GeV range. Its large
annihilation cross section due to the strong dynamics leaves the asymmetric
component to be dominant over the symmetric component. In such composite ADM
scenarios, the dark sector has a relatively large entropy density in the early
Universe. The large dark sector entropy results in the overclosure of the
Universe or at best contradicts with the observations of the cosmic microwave
background and the successful Big-Bang Nucleosynthesis. Thus, composite ADM
models generically require some portal to transfer the entropy of the dark
sector into the Standard Model sector. In this paper, we consider a dark photon
portal with a mass in the sub-GeV range and kinetic mixing with the Standard
Model photon. We investigate the viable parameter space of the dark photon in
detail, which can find broad applications to dark photon portal models. We also
provide a simple working example of composite ADM with a dark photon portal.
Our model is compatible with thermal leptogenesis and $B - L$ symmetry. By
taking into account the derived constraints, we show that the parameter space
is largely tested by direct detection experiments.
