Average and dispersion of the luminosity-redshift relation in the
  concordance model
  Starting from the luminosity-redshift relation recently given up to second
order in the Poisson gauge, we calculate the effects of the realistic
stochastic background of perturbations of the so-called concordance model on
the combined light-cone and ensemble average of various functions of the
luminosity distance, and on their variance, as functions of redshift. We apply
a gauge-invariant light-cone averaging prescription which is free from infrared
and ultraviolet divergences, making our results robust with respect to changes
of the corresponding cutoffs. Our main conclusions, in part already anticipated
in a recent letter for the case of a perturbation spectrum computed in the
linear regime, are that such inhomogeneities not only cannot avoid the need for
dark energy, but also cannot prevent, in principle, the determination of its
parameters down to an accuracy of order $10^{-3}-10^{-5}$, depending on the
averaged observable and on the regime considered for the power spectrum.
However, taking into account the appropriate corrections arising in the
non-linear regime, we predict an irreducible scatter of the data approaching
the 10% level which, for limited statistics, will necessarily limit the
attainable precision. The predicted dispersion appears to be in good agreement
with current observational estimates of the distance-modulus variance due to
Doppler and lensing effects (at low and high redshifts, respectively), and
represents a challenge for future precision measurements.
