  A new class of gravity-matter model defined with an independent
non-Riemannian volume form is studied, in the second order formalism. The
action has a global scale invariance symmetry, which can be broken by the
equation of motion of the measure fields. By a conformal transformation the
theory transforms into a theory which governed by two independent scalar fields
and a specific potential. When the scale invariance symmetry is not broken also
in the equations of motion, only one field appear in the effective potential.
This effective potential has a flat region which is responsible for the
inflation, and it ends with a minimum, which is responsible for the present
vacuum energy. In the general case, with a spontaneous symmetry breaking of the
scale symmetry, one scalar field is responsible for the inflation and the other
could be responsible for the particle creation. The first field (inflaton) can
slowly roll, while the second field (curvaton) is more strongly coupled to the
potential. The number of e-folds for both models is also dissuaded and could be
constraint in the future.
