Networks of cosmological histories, crossing of the phantom divide line and potentials with cusps

TL;DR

This paper explores how scalar field potentials with cusps can naturally induce smooth crossings of the phantom divide line in cosmological models, revealing a network of possible cosmic histories.

Contribution

It introduces the concept of cosmological histories network and analyzes the role of cusp potentials in enabling smooth phantom divide crossings.

Findings

Cusp potentials facilitate smooth crossing of the phantom divide line.

A network of cosmological histories is constructed and qualitatively analyzed.

A mechanical analogy helps understand the behavior near cusps.

Abstract

We discuss the phenomenon of the smooth dynamical gravity induced crossing of the phantom divide line in a framework of simple cosmological models where it appears to occur rather naturally, provided the potential of the unique scalar field has some kind of cusp. The behavior of cosmological trajectories in the vicinity of the cusp is studied in some detail and a simple mechanical analogy is presented. The phenomenon of certain complementarity between the smoothness of the spacetime geometry and matter equations of motion is elucidated. We introduce a network of cosmological histories and qualitatively describe some of its properties.