On the Quasi-Isotropic Inflationary Solution

TL;DR

This paper derives a quasi-isotropic inflationary model allowing inhomogeneities, showing that such inhomogeneities cannot significantly influence structure formation due to the inflationary dynamics, thus supporting the classical origin hypothesis of large-scale structures.

Contribution

It introduces a first-order inhomogeneous inflationary solution with an effective cosmological constant, extending the flat FRW model to include controlled inhomogeneities.

Findings

Inhomogeneities are negligible for structure formation due to inflation

The model allows arbitrary spatial distributions of matter and scalar fields

Inflation remains incompatible with a classical origin of large-scale structures

Abstract

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 generalize the (flat) FRW 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 $\eta(t)$. In a Universe filled with ultrarelativistic matter and a real self-interacting scalar field, we discuss the resulting dynamics, up to first order in $\eta$, 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 ultrarelativistic 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.