Inflation and cosmological constant

In construction of an inflationary model, one usually assumes that the matter sector of the gravitational action is minimally coupled to the background. It means that the matter (inflaton) part of the action is coupled with the same metric of the gravitational part. We elaborate on this assumption and investigate some of the consequences. We assume that the gravitational and the inflaton sectors belong to different units (or conformal frames). We show that this coupling can convert a single-field inflationary model into a two-field one with a mixed kinetic term. The energy-momentum tensor of the inflaton is therefore non-conserved due to the interaction with the conformal factor. This allows an energy exchange between the two fields and provides us with a mechanism for reduction of a large effective cosmological constant during inflation.