Averaging the luminosity redshift relation: from theory to observations

I will show a general covariant gauge invariant formalism for defining cosmological averages that are relevant for observations based on light-like signals. Afterwards, using such formalism, together with adapted "geodesic light-cone" coordinates, I will show as different effects emerge in the evaluation of observables related to the luminosity distance-redshift relation in an inhomogeneous Universe. To conclude, considering a realistic stochastic spectrum of inhomogeneities of primordial (inflationary) origin, I will show the magnitude and behaviour of such different effects, showing how such inhomogeneities cannot avoid the need for dark energy. On the other hand, taking into account the appropriate corrections arising in the non-linear regime, we predict an irreducible large scatter of the data, in particular at z>0.3 we obtain that the distance modulus lensing dispersion is very well captured by a linear behaviour which can be roughly fitted by \sigma_\mu^{lens}=0.056 z.