The Schrodinger picture of standard cosmology

TL;DR

This paper introduces a Schrödinger-like equation for cosmological inflation models, revealing that quantum bound states correspond to classical inflationary solutions, offering new insights into the dynamics of the universe.

Contribution

It establishes a novel quantum-mechanical framework for analyzing inflationary cosmology, connecting bound states to classical solutions in a flat FRW universe.

Findings

Quantum bound states correspond to classical inflationary solutions.

The approach provides a deeper understanding of inflation dynamics.

Exact solutions resemble known inflationary models.

Abstract

We consider a time independent Schrodinger type equation derived from the equations of motion that drives a single scalar field in a standard cosmology model for inflation in a flat space-time with a Friedman-Robertson-Walker (FRW) metric with a cosmological constant. We find that all the 1-dimensional bound state solutions of quantum mechanics lead to at least one exact solution for the dynamical equations of standard cosmology, and that these solutions resemble the most recurrent inflationary solutions found in the literature. The analogies derived from this approach may be used to realize a deeper understanding of the dynamics of the model.