Averaging the luminosity redshift relation: from theory to observations

In this seminar I will show a general 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. Our main conclusions are that such inhomogeneities cannot avoid the need for dark energy. 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.