An Inflationary Non-singular Quantum Cosmological Model

TL;DR

This paper develops a quantum cosmological model of a stiff matter universe, demonstrating non-singular inflationary solutions driven by quantum effects without requiring an inflaton, and analyzes their dynamics using the Bohm-de Broglie interpretation.

Contribution

It introduces a quantum cosmological model with non-singular inflationary solutions arising from a stiff matter universe, analyzed via generalized Gaussian superpositions and Bohmian trajectories.

Findings

Non-singular inflationary solutions starting from flat spacetime.

Quantum effects induce inflation without an inflaton.

Graceful exit from inflation to classical stiff matter expansion.

Abstract

A stiff matter-dominated universe modeled by a free massless scalar field minimally coupled to gravity in a Friedmann-Lema\^{\i}tre-Robertson-Walker (FLRW) geometry is quantized. Generalized complex-width gaussian superpositions of the solutions of the Wheeler-DeWitt equation are constructed and the Bohm-de Broglie interpretation of quantum cosmology is applied. A planar dynamical system is found in which a diversity of quantum bohmian trajectories are obtained and discussed. One class of solutions represents non-singular inflationary models starting at infinity past from flat space-time with Planckian size spacelike hypersurfaces, which inflates without inflaton but due to a quantum cosmological effect, until it makes an analytical graceful exit from this inflationary epoch to a decelerated classical stiff matter expansion phase.