Emergence of phantom cold dark matter from spacetime diffusion

A way to reconcile general relativity and quantum field theory without quantising the geometry is to demand the metric evolve stochastically. In this article, we explore the consequences of such a proposal at early cosmological times. We find the stochastic evolution results in the spatial metric diffusing away from its deterministic value, generating phantom cold dark matter (CDM). It is produced primarily at the end of the inflationary phase of the Universe's evolution, with a statistical distribution that depends on the specifics of the early-times cosmological model. We find the energy density of this phantom cold dark matter is positive on average, a necessary condition to reproduce the cosmological phenomenology of CDM, although further work is required to calculate its mean density and spatial distribution. If the density is cosmologically significant, phantom dark matter acts on the geometry in a way that is indistinguishable from conventional CDM. As such, it has the potential to reproduce phenomenology such as structure formation, lensing, and galactic rotation curves. We conclude by discussing the possibility of testing hybrid theories of gravity by combining measurements of the Cosmic Microwave Background with tabletop experiments.