Semiclassical cosmology with back reaction: the Friedmann-Schrodinger equation and inflation

Abstract

We propose and study a semi-classical cosmological system akin to the Newton-Schrödinger equation where matter field evolution is determined by time dependent Schrödinger equation. The resulting dynamics is one where the scale factor self-consistently informs the quantum evolution of the scalar field wave function via the Friedmann equation. We study various potentials, and show that for each case, inflation arises naturally, without fine-tuning, for arbitrary initial wave functions for the scalar field. Furthermore, due to zero-point quantum fluctuations of the scalar field, the equation of state $P=-ρ$ arises dynamically at late times for all initial states and potentials.

Punchline: Inflation is very likely to occur and is eternal. The paper has 15 pages and 3 figures