A Note on the Quality of Dilatonic Ultralight Dark Matter

Dilatons are pseudo-Nambu-Goldstone bosons arising from the breaking ofconformal invariance. In this letter we point out that in general a dilatonmass has a power-law dependence on a small parameter related to the explicitbreaking of conformal invariance whereas the ratio between the ultraviolet andinfrared scales in the theory are exponentially related to the same parameter.We show that this scaling results in a separation between the dilaton mass andthe infrared scale that can not be arbitrary large. Therefore a small dilatonmass necessarily is associated to a secluded conformal sector. We argue thatthe fact that the dilaton field must have a small displacement from the minimumof its effective potential generated near the infrared scale precludes acosmologically interesting amount of dilatonic dark matter to be produced by amisalignment mechanism in the early Universe.