Oscillatory Attractors: A New Cosmological Phase

TL;DR

This paper introduces a novel class of scalar field models in expanding cosmological spacetimes where the fields oscillate indefinitely, breaking time translation symmetry and potentially driving inflation or dark energy, with unique stability properties.

Contribution

The authors discover and analyze a new type of cosmological scalar field attractor that oscillates perpetually despite Hubble friction, differing from traditional static or relaxing solutions.

Findings

Fields oscillate indefinitely with finite amplitude in expanding spacetime.

Effective equation of state averages to -1, mimicking dark energy or inflation.

Low k-modes are stable, high k-modes are typically unstable.

Abstract

In expanding FRW spacetimes, it is usually the case that homogeneous scalar fields redshift and their amplitudes approach limiting values: Hubble friction usually ensures that the field relaxes to its minimum energy configuration, which is usually a static configuration. Here we discover a class of relativistic scalar field models in which the attractor behavior is the field oscillating indefinitely, with finite amplitude, in an expanding FRW spacetime, despite the presence of Hubble friction. This is an example of spontaneous breaking of time translation symmetry. We find that the effective equation of state of the field has average value $\langle w\rangle=-1$, implying that the field itself could drive an inflationary or dark energy dominated phase. This behavior is reminiscent of ghost condensate models, but in the new models, unlike in the ghost condensate models, the energy-momentum tensor is time dependent, so that these new models embody a more definitive breaking of time translation symmetry. We explore (quantum) fluctuations around the homogeneous background solution, and find that low $k$-modes can be stable, while high $k$-modes are typically unstable. We discuss possible interpretations and implications of that instability.