Quantum Backreaction in Finite and Infinite Cosmological Domains

Quantum backreaction may alter the local equivalence between a finite cosmological domain and an infinite extension with the same classical scalar response. This article derives a local criterion for matching renormalized stress tensors and identifies conditions that preserve the same geometry at first order. An explicit example shows how states with identical mean fields but different correlations produce distinct metric and curvature responses. This effect depends on quantum state data rather than finite volume alone.