Dominik Schwarz - the averaging problem ArXiv:0710.5073

• compare Hubble scale and comoving distances corresponding to 180deg and 60deg as a function of z - coincidence at around z ~ 1 or so ?
• BAO and SNeIa are local - SNeIa in the sense that without the z < 0.2 info the dataset loses a lot of its constraining power
• WMAP alone doesn't give
• volume averaging affects power spectrum P(k) !
• averaging time is over time cone volume, not comoving volume?
• "synchronous coordinates"
• can set in the effective Friedmann equation
• Li & Schwarz 2007: ArXiv:0710.5073
  • r < 30 Mpc @z=0 , also
  • curvature corrections less than 10% for r < 80 Mpc
  • Eq. (15) of 0710.5073 - 10% level at about 50Mpc, so above this the effects are relatively small
  • Fig. 2: this inhomogeneous modelling correctly fits the growth of the variance with z in the Freedman et al 2001 H_0 set of estimates, while variance calculated for a homogeneous model underestimates the variance
  • is the "peculiar gravitational potential", i.e. initial power spectrum, it does not have the radiation-matter turn over
  • idea: this method should be used when modelling H_0 in general, for the regions below about 150 Mpc
  • idea: some work done in this direction - consider how H_0 varies in different directions and model this inhomogeneously