Constraints on Mirror Models of Dark Matter from Observable Neutron-Mirror Neutron Oscillation

The process of neutron-mirror neutron oscillation, motivated by symmetric mirror dark matter models, is governed by two parameters: $n-n'$ mixing parameter $\delta$ and $n-n'$ mass splitting $\Delta$. For neutron mirror neutron oscillation to be observable, the splitting between their masses $\Delta$ must be small and current experiments lead to $\delta \leq 2\times 10^{-27}$ GeV and$\Delta \leq 10^{-24}$ GeV. We show that in mirror universe models where this process is observable, this small mass splitting constrains the way that one must implement asymmetric inflation to satisfy the limits of Big Bang Nucleosynthesis on the number of effective light degrees of freedom. In particular we find that if asymmetric inflation is implemented by inflaton decay to color or electroweak charged particles, the oscillation is unobservable. Also if one uses SM singlet fields for this purpose, they must be weakly coupled to the SM fields.