  The superhorizon (iso)curvature perturbations are conserved if the following
conditions are satisfied: (i) (each) non adiabatic pressure perturbation is
zero, (ii) the gradient terms are ignored, that is, at the leading order of the
gradient expansion (iii) (each) total energy momentum tensor is conserved. We
consider the case with the violation of the last two requirements and discuss
the generation of secondary isocurvature perturbations during the late time
universe. Second order gradient terms are not necessarily ignored even if we
are interested in the long wavelength modes because of the convolutions which
may pick products of short wavelength perturbations up. We then introduce
second order conserved quantities on superhorizon scales under the conditions
(i) and (iii) even in the presence of the gradient terms by employing the full
second order cosmological perturbation theory. We also discuss the violation of
the condition (iii), that is, the energy momentum tensor is conserved for the
total system but not for each component fluid. As an example, we explicitly
evaluate second order heat conduction between baryons and photons due to the
weak Compton scattering, which dominates the period just before recombination.
We show that such secondary effects can be recast into the isocurvature
perturbations on superhorizon scales if the local type primordial non
Gaussianity exists a priori.

Cosmology and Nongalactic Astrophysics;General Relativity and Quantum Cosmology;High Energy Physics - Phenomenology;High Energy Physics - Theory