  We explore a model of two-field inflation with nonminimal kinetic terms in
which two identical matter sectors decoupled from each other may reheat to
different temperatures while preserving the symmetry of the Lagrangian. This
scenario is motivated by mirror dark matter models in which the temperature of
the mirror sector is constrained to be $T'\lesssim0.5 T$ by big bang
nucleosynthesis and the cosmic microwave background. For a given class of
nonminimal kinematic terms, we find that the symmetric field trajectory $X=Y$
is a repeller solution, such that any randomly-occurring asymmetry in the
initial conditions is amplified by many orders of magnitude during inflation,
far beyond what canonical power-law models can achieve. Isocurvature
fluctuations are strongly suppressed in this model, but a $\mathcal
O(0.03$--$0.07$) tensor-to-scalar ratio could be observed in the near future.
The range of potential parameters compatible with {\it Planck} constraints is
shown to be much larger than in corresponding single-field models. This occurs
through a mechanism for lowering the spectral index that we dub CTHC: curved
trajectory at horizon crossing.
