In this paper we find a solution for a quasi-isotropic inflationary Universe which allows to introduce in the problem a certain degree of inhomogeneity. We consider a model which generalizes the (flat) FLRW one by introducing a first order inhomogeneous term, whose dynamics is induced by an effective cosmological constant. The 3-metric tensor is constituted by a dominant term, corresponding to an isotropic-like component, while the amplitude of the first order one is controlled by a "small" function η(t). In a Universe filled with ultra relativistic matter and a real self-interacting scalar field, we discuss the resulting dynamics, up to first order in η, when the scalar field performs a slow roll on a plateau of a symmetry breaking configuration and induces an effective cosmological constant. We show how the spatial distribution of the ultra relativistic matter and of the scalar field admits an arbitrary form but nevertheless, due to the required inflationary e-folding, it cannot play a serious dynamical role in tracing the process of structures formation (via the Harrison–Zeldovic spectrum). As a consequence, this paper reinforces the idea that the inflationary scenario is incompatible with a classical origin of the large scale structures.
The magnetic Scott correction for relativistic matter at criticality
