Covariant HeatFlow Vacuum Response, Conserved Stress Tensors, and a Minimal Cosmological Model

This research note develops a minimal covariant model of curvature-controlled vacuum response. A dimensionless response field \(\chi\) is introduced in a localized Jordan-frame scalar-tensor action, yielding an effective vacuum stress tensor that is covariantly conserved on shell.

The model screens stationary de Sitter curvature while allowing dynamical departures from equilibrium to act as a finite gravitational source. In a spatially flat FRW background, the nonlinear system admits a large-\(\chi\) slow-relaxation branch with \(\epsilon_H\simeq 1/\chi^2\), producing an inflation-like phase and a natural dynamical exit without introducing a separate inflaton field.

A stable interaction \(g^2\chi^2\phi^2\) with an inhomogeneous scalar sector is used to study post-exit classical-statistical preheating. Representative simulations show selective finite-momentum mode amplification and temporary matter-sector domination, though a fully radiation-like or thermalized state is not yet established.

The framework is proposed as a possible unified effective description of vacuum screening, inflation-like relaxation, exit, preheating, and late-time residual vacuum response. The microscopic origin of the covariant HeatFlow response and the renormalized semiclassical extension are left for future work.