Mimetic Dark Matter from Inflation

TL;DR

This work investigates generating mimetic dark matter during inflation by coupling the mimetic field to the Gauss–Bonnet topological invariant. By choosing a simple linear coupling $f(\phi)=\beta\phi$ and $g(\kappa)=\kappa^{3}$, the authors show that a dust-like DM component arises with an energy density set by the Hubble parameter at the end of inflation, and they provide a clear expression for the DM–radiation equality timing. They also explore nonlinear couplings that yield anomalous DM behavior during DM domination, illustrating how the expansion history can be modified without introducing ghosts. Overall, the framework offers a geometrical, unitary mechanism for DM production tied to early-universe dynamics, with potential implications for singularity resolution and covariant reformulations of related gravity theories.

Abstract

We investigate the coupling of mimetic dark matter to the Gauss-Bonnet topological term in addition to the Einstein-Hilbert action. We demonstrate that such interactions can naturally give rise to mimetic dark matter during the inflationary stage of the universe's evolution. By choosing an appropriate coupling between the mimetic field and the Gauss-Bonnet term, we find that at the end of inflation, the correct amount of dust-like dark matter is produced, with its energy density expressible in terms of the Hubble parameter at the end of inflation. Furthermore, depending on the form of the coupling, the post matter-radiation equality behavior of mimetic dark matter can experience slight modifications.