Dark Matter From Spacetime Nonlocality

Abstract

We propose that dark matter is not yet another new particle in nature, but that it is a remnant of quantum gravitational effects on known fields. We arrive at this possibility in an indirect and surprising manner: by considering retarded, nonlocal, and Lorentzian evolution for quantum fields. This is inspired by recent developments in causal set theory, where such an evolution shows up as the continuum limit of scalar field propagation on a background causal set. Concretely, we study the quantum theory of a massless scalar field whose evolution is given not by the the d'Alembertian $\Box$, but by an operator $\tilde \Box$ which is Lorentz invariant, reduces to $\Box$ at low energies, and defines an explicitly retarded evolution: $(\tilde \Box ϕ)(x)$ only depends on $ϕ(y)$, with $y$ is in the causal past of $x$. This modification results in the existence of a continuum of massive particles, in addition to the usual massless ones, in the free theory. When interactions are introduced, these massive or off-shell quanta can be produced by the scattering of massless particles, but once produced, they no longer interact, which makes them a natural candidate for dark matter.