Backreaction: Gauge and Frame Dependences
  The cosmological backreaction from perturbations is clearly gauge-dependent,
and obviously depends on the choice of averaged Hubble rate. We consider two
common choices of Hubble rate and advocate the use of comoving
volume-preserving gauges. We highlight two examples valid to an appropriate
order in perturbation theory, uniform curvature gauge, which is as close to
volume-preserving as possible, and a spatially-traceless uniform cold dark
matter gauge which preserves the volume to linear order. We demonstrate the
strong gauge- and frame-dependences in averaging. In traceless uniform CDM
gauge the backreaction exhibits a strong ultra-violet divergence and can be
tuned to an arbitrary magnitude with an appropriate choice of smoothing scale.
In uniform curvature gauge we find that for a choice of Hubble rate locked to
the spatial surface the backreaction vanishes identically, while for a Hubble
rate defined from a fluid's expansion scalar the effective energy density at
the current epoch in an Einstein-de Sitter universe is Omega_eff~5e-4, slightly
bigger than but in broad agreement with previous results in conformal Newtonian
gauge.
