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arXiv · 2604.01047

The Semiclassical Einstein-Klein-Gordon System: Asymptotic Analysis of Minkowski Spacetime

Stefano Galanda·Paolo Meda·Simone Murro·Nicola Pinamonti·Gabriel Schmid
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Abstract

We establish the linear instability of the semiclassical Einstein-Klein-Gordon system linearised about the Minkowski vacuum spacetime. The proof relies on formulating a forcing problem for both metric and state perturbations within the space of past-compact sections. This geometric framework admits a unique tensor decomposition which, in conjunction with the quantum M{\o}ller operator, enables the decoupling of the linearised system into two distinct Cauchy problems. Consequently, the metric perturbations are shown to be governed by a higher-order, nonlocal hyperbolic partial differential equation. By relegating the nonlocal contributions to subleading order, we establish the well-posedness of this forcing problem. Furthermore, we provide a rigorous asymptotic analysis for physically admissible choices of the renormalisation constants. We prove that the system exhibits a late-time linear instability: the metric perturbations grow exponentially, bounded strictly by a universal scale H, thereby indicating a quantum backreaction-driven transition toward a de Sitter cosmological spacetime. Provided the parameters governing the system are restricted to a physically relevant regime, this universal scale is compatible with the measured expansion of our universe.

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Stefano Galanda, Paolo Meda, Simone Murro, Nicola Pinamonti, Gabriel Schmid. 2026-04-01. The Semiclassical Einstein-Klein-Gordon System: Asymptotic Analysis of Minkowski Spacetime. https://arxiv.org/abs/2604.01047

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