Cosmological Classical Branches: Operational classicality of primordial curvature perturbations from late-time matter records

This paper addresses a fundamental unresolved problem in inflationary cosmology: what quantum-state structure makes the one-realization classical description used in late-time cosmology physically meaningful within unitary quantum theory? We identify a structure that supports such a description, which we call Cosmological Classical Branches (CCBs). After reheating, the curvature perturbation is a collective variable rather than an independent subsystem. This shifts the classicality problem from the reduced state of the curvature perturbation itself to records of primordial information in the post-reheating matter state. When distinct matter components respond to the same primordial realization and their conditional states become distinguishable across different realizations, they carry records of the information about the curvature perturbation. A record in one component makes the realization readable, while a compatible record in a disjoint component suppresses interference accessible to operations confined to the first component, forming CCBs. Conditioning on a physical record yields a one-realization description within a CCB, in which the resolved primordial value acts as a c-number label while the matter degrees of freedom remain quantum. We test this criterion using effective models of two radiation fluids during radiation domination and of photons and cold dark matter around radiation--matter equality. We also show that a CCB typical with respect to the primordial Born measure exhibits the expected one-realization statistics: mode averages approach the primordial two-point statistics at fixed nonzero wavenumber in the large-volume limit. Overall, these results provide an operational framework at the quantum-state level connecting the primordial quantum superposition to the one-realization cosmological history assumed in standard cosmology.