Inhomogeneous de Sitter Solution with Scalar Field and Perturbations Spectrum

We provide an inhomogeneous solution concerning the dynamics of a real self interacting scalar field minimally coupled to gravity in a region of the configuration space where it performs a slow rolling on a plateau of its potential. During the inhomogeneous de Sitter phase the scalar field dominant term is a function of the spatial coordinates only. This solution specialized nearby the FLRW model allows a classical origin for the inhomogeneous perturbations spectrum.