| Abstract: | The combination of CMB anisotropies measurements, large scale structure (LSS) observations and type Ia supernovae has led to the emergence of the concordance model of cosmology, where ~73% of the critical energy density is attributed to a cosmological constant/ Dark energy/ Modified gravity. The model is based on assuming FLRW metric with perturbations. In CMB and LSS analysis the perturbations have been taken into account and are crucial for both the CMB anisotropies and the existence of clusters, galaxies, stars etc. However, In the case of supernovae type Ia, i.e. the luminosity distance-redshift relation, the perturbations have been discarded completely. We compute the effect of a stochastic background of cosmological perturbations on the luminosity-redshift relation is computed to second order through a recently proposed covariant and gauge-invariant light-cone averaging procedure. The resulting expressions are free from both ultraviolet and infrared divergences, implying that such perturbations cannot mimic a sizeable fraction of dark energy. Different averages are estimated and depend on the particular function of the luminosity distance being averaged. The energy flux, being minimally affected by perturbations at large z, is proposed as the best choice for precision estimates of dark-energy parameters. Nonetheless, its irreducible (stochastic) variance induces statistical errors on (z) typically lying in the few-percent range. |
