Cosmology With Negative Potentials

TL;DR

This paper explores cosmological models with negative potentials, revealing new phase space features, analyzing their evolution, and addressing challenges in cyclic universe scenarios, proposing modifications including an inflation stage.

Contribution

It introduces new phase portrait features for models with negative potentials and evaluates the cyclic universe scenario, suggesting improvements with an inflation stage.

Findings

Cosmological models with negative potentials have unique phase space features.

Universes with negative potential minima reach a turning point before contraction.

Adding inflation after singularity can improve cyclic universe models.

Abstract

We investigate cosmological evolution in models where the effective potential V(\phi) may become negative for some values of the field \phi. Phase portraits of such theories in space of variables (\phi,\dot\phi,H) have several qualitatively new features as compared with phase portraits in the theories with V(\phi) > 0. Cosmological evolution in models with potentials with a "stable" minimum at V(\phi)<0 is similar in some respects to the evolution in models with potentials unbounded from below. Instead of reaching an AdS regime dominated by the negative vacuum energy, the universe reaches a turning point where its energy density vanishes, and then it contracts to a singularity with properties that are practically independent of V(\phi). We apply our methods to investigation of the recently proposed cyclic universe scenario. We show that in addition to the singularity problem there are other problems that need to be resolved in order to realize a cyclic regime in this scenario. We propose several modifications of this scenario and conclude that the best way to improve it is to add a usual stage of inflation after the singularity and use that inflationary stage to generate perturbations in the standard way.