  Mirror models lead to the possibility that neutron ($n$) can oscillate into
its mirror partner ($n'$) inspiring several experimental searches for this
phenomenon. The condition for observability of this oscillation is a high
degree of degeneracy between the $n$ and $n'$ masses, which can be guaranteed
if there is exact parity symmetry taking all particles to their mirror
partners. However consistency of these models with big bang nucleosynthesis
requires that this parity symmetry be broken in the early universe in a
scenario called asymmetric inflation. In this paper we study the consistency of
an observable $n-n'$ oscillations signal with asymmetric inflation and derive
various theoretical constraints. In particular, we find that the reheat
temperature after inflation should lie below 2.5 TeV, and predict a singlet
fermion with a mass below 100 GeV. In simple models where the right-handed
neutrino is a mediator of baryon number violating interactions we find that the
light neutrinos are Dirac fermions with their masses arising radiatively
through one-loop diagrams.
