Anomalous contribution to galactic rotation curves due to stochastic spacetime
arxiv(2024)
摘要
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 acts 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 how this modifies the expectation value of the metric via the path
integral formalism, and find that an entropic force driven by a stochastic
cosmological constant can explain galactic rotation curves without needing to
evoke 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.
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