Metric emerging to massive modes in quantum cosmological space-times

TL;DR

This paper demonstrates that quantum effects cause anisotropy in the semi-classical metric experienced by a massive Klein-Gordon field mode in an isotropic quantum cosmological background, revealing quantum-induced directional dependence.

Contribution

It introduces a method to derive emergent semi-classical metrics from quantum cosmological backgrounds, highlighting quantum anisotropies in an isotropic setting.

Findings

Quantum anisotropy depends on mode momentum direction.

Emergent metric components are derived from quantum field propagation.

Anisotropies are proportional to Planck constant, indicating quantum origin.

Abstract

We consider a massive quantum test Klein-Gordon field probing an isotropic quantum cosmological space-time in the background. The result obtained is surprising. It turns out, that despite the isotropy of the quantum gravitational field, the semi-classical metric experienced by a mode of the K-G field is non-isotropic. The anisotropy depends on the direction of the momentum of the mode. Specifically, what we do is to derive a semi-classical space-time which emerges to a mode of the field. The method amounts to a comparison between QFT on a quantum background and QFT on a classical curved space-time, giving rise to an emergent metric tensor. The components of the semi-classical metric tensor are calculated from the equation of propagation of the quantum K-G field in the test field approximation. The anisotropies are of a quantum nature: they are proportional to Planck constant and "dress" the isotropic classical space-time obtained in the classical limit.