  Mirror dark matter interacting with ordinary matter via photon-mirror photon
kinetic mixing can explain the DAMA, CoGeNT and CRESSTII direct detection
experiments. This explanation requires kinetic mixing of strength $\epsilon
\sim 10^{-9}$. Such kinetic mixing will have important implications for early
Universe cosmology. We calculate the additional relativistic energy density at
recombination, $\delta N_{eff} [CMB]$. We also calculate the effects for big
bang nucleosynthesis, $\delta N_{eff} [BBN]$. Current hints that both $\delta
N_{eff} [CMB]$ and $\delta N_{eff} [BBN]$ are non-zero and positive can be
accommodated within this framework if $\epsilon \approx few \times 10^{-9}$. In
the near future, measurements from the Planck mission will either confirm these
hints or constrain $\epsilon \stackrel{<}{\sim} 10^{-9}$.
