Spatial and temporal tuning in void models for acceleration
  There has been considerable interest in recent years in cosmological models
in which we inhabit a very large, underdense void as an alternative to dark
energy. A longstanding objection to this proposal is that observations limit
our position to be very close to the void centre. By selecting from a family of
void profiles that fit supernova luminosity data, we carefully determine how
far from the centre we could be. To do so, we use the observed dipole component
of the cosmic microwave background, as well as an additional stochastic
peculiar velocity arising from primordial perturbations. We find that we are
constrained to live within 80 Mpc of the centre of a void--a somewhat weaker
constraint than found in previous studies, but nevertheless a strong violation
of the Copernican principle. By considering how such a Gpc-scale void would
appear on the microwave sky, we also show that there can be a maximum of one of
these voids within our Hubble radius. Hence, the constraint on our position
corresponds to a fraction of the Hubble volume of order 10^{-8}. Finally, we
use the fact that void models only look temporarily similar to a
cosmological-constant-dominated universe to argue that these models are not
free of temporal fine-tuning.
