  We study polarized Gowdy cosmologies on the three torus coupled to a massive
scalar field. The phase space of the model admits a simple splitting between
homogeneous and inhomogeneous sectors after a suitable gauge fixing. The
presence of the mass term of the scalar field breaks the linearity of the
equations of motion of the inhomogeneous fields. We discuss regimes of physical
interest in which we recover a linear dynamics of these nonperturbative
inhomogeneities, despite the metric is fully inhomogeneous at early times. We
expand the inhomogeneous fields in Fourier modes and express them at all times
as linear combinations of a basis of orthonormal complex solutions to the
equations of motion, with coefficients that turn out to be an infinite
collection of constants of motion. We argue that the resulting model can
describe a nonperturbative inhomogeneous early universe dominated by the
kinetic energy of an inflaton at early times that can eventually reach a
slow-roll regime with a nearly exponential expansion at late times that
isotropices and homogenizes the geometry.
