The Phantom of the New Oscillatory Cosmological Phase

Abstract

We study a recently proposed new cosmological phase where a scalar field moves periodically in an expanding spatially-flat Friedmann universe. This phase corresponds to a limiting cycle of the equations of motion and can be considered as a cosmological realization of a "time-crystal". We show that this phase is only possible, provided the Null Energy Condition is violated and the so-called Phantom divide is crossed. We prove that in general k-essence models: i) this crossing causes infinite growth of quantum perturbations on short scales, and ii) exactly periodic solutions are only possible, provided the limiting cycle encircles a singularity in the phase plane. The configurations neighboring this singular curve in the phase space are linearly unstable on one side of the curve and superluminal on the other side. Moreover, the increment of the instability is infinitely growing for each mode by approaching the singularity, while for the configurations on the other side, the sound speed is growing without limit. We illustrate our general results by analytical and numerical studies of a particular class of such k-essence models.

arXiv comment15 pages, 3 figures, plus references

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Cited by in corpus (7)

• Scalar and Tensor Perturbations in DHOST Bounce Cosmology
• Unitary null energy condition violation in $P(X)$ cosmologies
• Toward an Effective Field Theory Approach to Reheating
• General dynamical properties of cosmological models with nonminimal kinetic coupling
• Birth of de Sitter Universe from time crystal
• Phantom Dirac-Born-Infeld Dark Energy
• Cosmic acceleration from string induced Galileons