Dilatonic Couplings and the Relic Abundance of Ultralight Dark Matter

Models of scalar field dark matter where the scalar is a dilaton have a special behaviour, since non-trivial couplings, $d$, to matter result in a contribution to the potential for the field which is proportional to the trace of the stress-energy tensor. We look in more detail at the dilaton mass, $m_\phi$, and initial conditions required to yield the correct relic abundance for couplings that are not already excluded by terrestrial experiments. In minimal models with only couplings accessible to terrestrial searches, we find that dilaton dark matter with $m_{\phi} \gtrsim 10^{-10}$ eV requires couplings suppressed compared to constraints from equivalence principle (EP) tests and fifth force searches in order to not produce too much dark matter, improving on the strongest current experimental constraints by up to $\sim {\cal O}(10)$, with consequences for the proposed mechanical resonator dilaton DM searches. In non-minimal or universally coupled models, the unconstrained couplings of the dilaton to e.g. the top quark can strongly influence the relic abundance at all masses. In particular, this implies that atom interferometry searches at masses $m_\phi\approx 10^{-19}\text{ eV}$ are unable to constrain the early Universe behaviour or UV physics of the dilaton. We also find that dilatonic couplings allow for compatibility of $m_\phi \gtrsim 10^{-7}\text{ eV}$ with an observably large tensor-to-scalar ratio in the cosmic microwave background, which is not possible for a decoupled scalar of the same mass.