Global stability of Minkowski spacetime for a causal nonlocal gravity model

Abstract

We establish small-data global existence and decay for the causal-informational nonlocal gravity model CETOmega in 3+1 dimensions. Under harmonic gauge the field equations reduce to a quasilinear hyperbolic system with causal memory generated by a retarded Stieltjes operator K^{-1}. We establish three results: (i) commutator estimates for the Klainerman vector fields acting on K^{-1}, showing that the nonlocal operator costs at most two additional derivatives relative to Einstein vacuum; (ii) a sharp Sobolev-level bound on the memory convolution under explicit integrability conditions on the spectral density rho; (iii) global existence, uniform energy bounds, and pointwise (1+t)^{-1} decay for small initial data in H^N with N>=10. The proof combines the Lindblad-Rodnianski ghost weight method with commutator estimates and resolvent identities adapted to the Stieltjes kernel. A key structural observation is that retarded causality of the kernel is mathematically necessary for the stability argument: acausal modifications destroy the hyperbolic energy identity on which the bootstrap relies. We verify that the spectral conditions are satisfied by explicit, physically motivated kernel families. Because the memory operator generates a persistent tail that does not vanish at late times, classical scattering to free waves does not hold; we establish instead modified scattering, proving convergence to a solution of a linear wave equation with an explicit, computable memory profile in the energy topology. We discuss quantitative observational signatures including gravitational wave memory excess, frequency-dependent phase shift, and anomalous late-time ringdown tail controlled by the same spectral constants governing the stability conditions.