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We investigate the late-time cosmological behaviour of scalar-tensor theorieswith a universal multiplicative coupling between the scalar field and thematter Lagrangian in the matter era. This class of theory encompasses the caseof the massless string dilaton (see Damour and Polyakov, General Relativity andGravitation, 26, 1171) as well as a theory with an intrinsic decouplingmechanism in the solar system (see Minazzoli and Hees, Phys. Rev. D 88,041504). The cosmological evolution is studied in the General Relativity limitjustified by solar system constraints on the gravitation theory. The behaviourof these cosmological evolutions are then compared to two types ofobservations: the constraints on temporal variations of the constants of Natureand the distance-luminosity measurements. In particular, the non-minimalcoupling implies that the distance-luminosity relation is modified compared toGeneral Relativity. Theories producing a cosmological behaviour in agreementwith these observations are identified.

Late-time cosmology of scalar-tensor theories with universal multiplicative coupling between the scalar field and the matter Lagrangian