required to explain it. Among them, a scalar field seems a good alternative although it is not the only one: higher order theories[@CotMir97; @Fed00] or dissipative fluid[@ChiJakPav00; @SenSen00] also give birth to inflationary behaviour. Scalar fields are required by standard model for elementary particles as well as by unification theories for which, for instance, compactification schemes[@EllKalOliYok99; @Wan94] are considered. These last theories also give a natural order of magnitude for the cosmological constant[@WesLiu01] at early times which may be 55 to 120 orders of magnitude bigger than its present observed value: this is the so-called cosmological constant problem. A solution is to consider that this “constant” varies across the Universe history. A massive scalar field is then an interesting possibility to simulate such a mechanism. All these elements show the interest of a minimally coupled scalar-tensor theory with a Brans-Dicke coupling function $\omega$ and a potential $U$ depending on the scalar field $\phi$.

What about the geometrical framework of this paper? FLRW models geometrically describe the observed homogeneity and isotropy of our Universe. However they are very special ones among the set of all possible models and do not allow to explain the observed large-scale structures. Moreover, at early times, 