Dark energy, scalar–curvature couplings and a critical acceleration scale

Abstract

We study the effects of coupling a cosmologically rolling scalar field to higher-ordercurvature terms. We show that when the strong coupling scale of the theory is on the10−3–10−1 eV range, the model passes all experimental bounds on the existence of fifth forces even ifthe field has a mass of the order of the Hubble scale in vacuum and non-suppressedcouplings to SM fields. The reason is that the coupling to a certain curvature invariant actsas an effective mass that grows in regions of large curvature. This prevents the fieldfrom rolling down its potential near sources and makes its effects on fifth-forcesearch experiments performed in the laboratory to be observable only at thesubmillimeter scale. We obtain the static spherically symmetric solutions of thetheory and show that a long-range force appears but it is turned on only belowa fixed Newtonian acceleration scale of the order of the Hubble constant. Wecomment on the possibility of using this feature of the model to alleviate the colddark matter (CDM) small-scale crisis and on its possible relation to MOND.