Modifying Gravity in the Infra-Red by imposing an "Ultra-Strong" Equivalence Principle

TL;DR

This paper proposes a theoretical modification of gravity at large scales by extending the equivalence principle to quantum phenomena, using infra-red modified commutation relations to eliminate local gravitational effects.

Contribution

It introduces a novel framework that extends the equivalence principle to quantum effects, modifying commutation relations to confine gravity to infra-red scales without adding new parameters.

Findings

Infra-red modifications reabsorb vacuum stress-energy divergences.

The approach confines gravitational effects to large scales.

No new dimensional parameters are introduced.

Abstract

The equivalence principle suggests to consider gravity as an infra-red phenomenon, whose effects are visible only outside Einstein's free-falling elevator. By curving spacetime, General Relativity leaves the smallest systems free of classical gravitational effects. However, according to the standard semi-classical treatment, indirect effects of gravity can be experienced inside the elevator through the well-known mechanism of quantum particle production. Here we try a different path than the one historically followed: rather than imposing field quantization on top of a curved manifold, we attempt to upgrade the equivalence principle and extend it to the quantum phenomena. Therefore, we consider, and try to realize in a theoretical framework, a stronger version of the equivalence principle, in which all the effects of gravity are definitely banned from the elevator and confined to the infra-red. For this purpose, we introduce infra-red modified commutation relations for the global field operators (Fourier modes) that allow to reabsorb the time-dependent quadratic divergence of the vacuum expectation value of the stress-energy tensor. The proposed modification is effective on length scales comparable to the inverse curvature and, therefore, does no add any dimensional parameter to the theory.