Oscillatory Attractors: A New Cosmological Phase
  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.
