Cosmology With Negative Potentials

TL;DR

Problem: what happens when the scalar field potential can be negative (V0<0) in cosmology and can such models support inflation or cyclic behavior? Approach: analyze the dynamics with phase portraits and classify four regimes, then apply to cyclic-universe ideas. Findings: negative potentials with a minimum below zero (V0<0) lead to a turning point and contraction to a singularity rather than AdS expansion; cyclic models face additional problems and require modifications such as inserting a standard inflationary stage after the singularity to generate perturbations. Significance: clarifies the viability of cyclic cosmologies with negative potentials and suggests that inflation may be essential even in these nonstandard scenarios.

Abstract

We investigate cosmological evolution in models where the effective potential V(φ) may become negative for some values of the field φ. Phase portraits of such theories in space of variables (φ,\dotφ,H) have several qualitatively new features as compared with phase portraits in the theories with V(φ) > 0. Cosmological evolution in models with potentials with a "stable" minimum at V(φ)<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(φ). 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.