Geodesically Complete Analytic Solutions for a Cyclic Universe

TL;DR

This paper derives analytic, geodesically complete cyclic universe solutions within scalar field cosmology, inspired by 2T-physics and M-theory, revealing conditions for bouncing universes and their quantum implications.

Contribution

It introduces new analytic solutions for cyclic universes with bounces, constrained by geodesic completeness, and connects these solutions to 2T-physics and M-theory frameworks.

Findings

Multiple geodesically complete cyclic solutions identified.

Constraints on model parameters for zero-size bounces.

Potential links between classical solutions and quantum Wheeler-deWitt states.

Abstract

We present analytic solutions to a class of cosmological models described by a canonical scalar field minimally coupled to gravity and experiencing self interactions through a hyperbolic potential. Using models and methods inspired by 2T-physics, we show how analytic solutions can be obtained in flat/open/closed Friedmann-Robertson-Walker universes. Among the analytic solutions, there are many interesting geodesically complete cyclic solutions in which the universe bounces at either zero or finite sizes. When geodesic completeness is imposed, it restricts models and their parameters to a certain parameter subspace, including some quantization conditions on initial conditions in the case of zero-size bounces, but no conditions on initial conditions for the case of finite-size bounces. We will explain the theoretical origin of our model from the point of view of 2T-gravity as well as from the point of view of the colliding branes scenario in the context of M-theory. We will indicate how to associate solutions of the quantum Wheeler-deWitt equation with our classical analytic solutions, mention some physical aspects of the cyclic solutions, and outline future directions.