Anomalous contribution to galactic rotation curves due to stochastic spacetime

TL;DR

This paper proposes that stochastic fluctuations in a classical spacetime metric can modify gravity at low accelerations, potentially explaining galactic rotation curves without dark matter through an entropic force effect.

Contribution

It introduces a stochastic spacetime model where metric fluctuations lead to low-acceleration modifications of general relativity, offering an alternative explanation for galactic rotation curves.

Findings

Stochastic spacetime induces an anomalous acceleration component.

The model predicts a cosmological constant-like contribution.

Potential for explaining galactic rotation curves without dark matter.

Abstract

We consider a proposed alternative to quantum gravity, in which the spacetime metric is treated as classical, even while matter fields remain quantum. Consistency of the theory necessarily requires that the metric evolve stochastically. Here, we show that this stochastic behaviour leads to a modification of general relativity at low accelerations. In the low acceleration regime, the variance in the acceleration produced by the gravitational field is high in comparison to that produced by the Newtonian potential, and can act as an entropic force, causing a deviation from Einstein's theory of general relativity. We show that in this "diffusion regime", the entropic force acts from a gravitational point of view, as if it were a contribution to the matter distribution. We compute modifications to the expectation value of the metric via the path integral formalism, and find an anomalous contribution which corresponds to a cosmological constant, anti-correlated with a contribution which has been used to fit galactic rotation curves without dark matter. We caution that a greater understanding of this effect is needed before conclusions can be drawn, most likely through numerical simulations, and provide a template for computing the deviation from general relativity which serves as an experimental signature of the Brownian motion of spacetime.