Dynamical dark energy from spacetime-symmetry breaking -- late-time behaviour and phantom crossing

We investigate the late-time cosmological dynamics in a simple case of explicit spacetime-symmetry breaking. By expanding in a small symmetry-breaking coefficient we are able to write the Friedmann equations as $\Lambda$CDM + dynamical dark energy, which we show contains logarithmic dependence of the scale factor. We find that the dark energy equation of state displays divergencies and phantom behaviour for certain values of the symmetry-breaking coefficient, where the NEC is also broken. We discuss the adiabatic sound speed of dark energy and compare the model to current constraints using the Chevallier-Polarski-Linder parametrisation. Remarkably, although the constraints on the same symmetry-breaking coefficient from e.g. gravitational-wave propagation are orders of magnitude stronger than what we obtain in this paper, we are able to cut those constraints, which are more or less symmetric around zero, in half by showing that same coefficient must be negative (or zero) if one wishes to keep the NEC intact.
Comment: Clarifications, analysis and references added, slight notation change. Accepted for publication in Physics of the Dark Universe