Very light cosmological scalar fields from a tiny cosmological constant

I discuss a mechanism which generates a mass term for a scalar field in an expanding universe. The mass of this field turns out to be generated by the cosmological constant and can be naturally small if protected by a conformal symmetry which is, however, broken in the gravitational sector. The mass is comparable today to the Hubble time. This scalar field could thus impact our Universe today and, for example, be at the origin of a time variation of the couplings and masses of the parameters of the standard model