Emergent Gravity via Causal Smoothing of the Vacuum Substrate

Abstract We present a covariant effective field theory in which spacetime curvature is reinterpreted not as a fundamental geometric interaction, but as the macroscopic, coarse-grained, retarded linear response of a microscopic quantum vacuum substrate. By applying an Ohmic spectral density to filter high-frequency vacuum modes, we derive a collective, dimensionless scalar strain field 𝑞(𝑥) coupled non-minimally to the Ricci scalar. The model introduces a novel nonlinear curvature constitutive law governed by an asymptotic curvature scale 𝑅ₘₐₓ, ensuring that deviations from General Relativity are parametrically suppressed in weak-field regimes. The resulting macroscopic action maps to a stable, higher-derivative-free Horndeski scalar-tensor theory. Cosmologically, the framework naturally admits a stable, late-time de Sitter vacuum state where the effective equation of state is exactly 𝑤 = −1, providing a purely collective mechanism for dark energy without a finely tuned zero-point energy. Furthermore, the conformal coupling structure rigorously preserves luminal tensor propagation speeds (𝑐_𝑇 = 𝑐), fully satisfying multi-messenger constraints from GW170817. Simultaneously, it predicts a modified gravitational-wave luminosity distance due to scalar-induced amplitude damping, a signature directly testable by next-generation standard siren observations. Finally, an analysis of the static, spherically symmetric strong-field regime reveals that while local expansions yield a regular de Sitter core with finite curvature invariants, global Einstein-frame integration proves that this scalar-tensor truncation conforms to generalized no-hair theorems. Consequently, the theory yields an exactly Schwarzschild exterior, highlighting the necessary boundary parameters for future microscopic spin-2 completions.