We present a general gauge invariant formalism for defining cosmological averages that are relevant for observations based on light-like signals. Such averages involve either null hypersurfaces corresponding to a family of past light-cones or compact surfaces given by their intersection with timelike hypersurfaces. Generalized Buchert-Ehlers commutation rules for derivatives of these light-cone averages are given. After introducing some adapted "geodesic light-cone" coordinates, we give explicit expressions for averaging the redshift to luminosity-distance relation and the so-called "redshift drift" in a generic inhomogeneous Universe.

Using a recently proposed gauge invariant formulation of light-cone averaging, together with adapted "geodesic light-cone" coordinates, we show how an "induced backreaction" effect emerges, in general, from correlated fluctuations in the luminosity distance and covariant integration measure. Considering a realistic stochastic spectrum of inhomogeneities of primordial (inflationary) origin we find that both the induced backreaction on the luminosity-redshift relation and the dispersion are larger than naïvely expected. On the other hand the former, at least to leading order and in the linear perturbative regime, cannot account by itself for the observed effects of dark energy at largeredshifts. A full second-order calculation, or even better a reliable estimate of contributions from the non-linear regime, appears to be necessary before firm conclusions on the correct interpretation of the data can be drawn. PACS numbers: 98.80-k, 95.36.+x, 98.80.Es I. INTRODUCTIONThe so-called concordance (or ΛCDM) model, based on a suitable combination of dark matter, dark energy and baryons for an overall critical density, has become the reference paradigm for the late -i.e. post-equality epochevolution of our Universe (see e.g. [1]). It accounts equally well for the CMB data, the Large Scale Structure and, even more significantly, for the supernovae data in terms of a cosmic acceleration [2].Strictly speaking these three tests of the concordance model are not at the same level of theoretical rigor. While the first two have to do, by definition, with the inhomogeneities present in our Universe, the third is based on an ideal homogeneous and isotropic Friedmann-Lemaître-Robertson-Walker (FLRW) geometry. It is clear that a better treatment of cosmic acceleration should take inhomogeneities into account, at least in an average statistical sense. Only when this is done we can establish in a convincing way whether ΛCDM gives a simultaneous consistent description of the above-mentioned body of cosmological data.This realization has led to a vast literature about averaging cosmological observables in realistic inhomogeneous cosmologies (see e.g. [3] for recent reviews). The conclusions, however, are still rather controversial: according to some authors [4] present inhomogeneities might explain, by themselves, cosmic acceleration without any need for dark-energy contributions; according to others [5] the effect of inhomogeneities is, instead, completely negligible. The truth may lie somewhere in between, in the sense that a quantitative understanding of inhomogeneities effects could be important in order to put precise constraints on dark-energy parameters, such as the critical fraction of dark-energy density, Ω Λ , and the time evolution of its effective equation of state, w Λ (z).In the first papers studying the dynamical effects of averaging, the problem was approached mainly following Buchert's prescriptions [6], namely averaging inhomogeneities over spacelike hypersurfaces and computing the ensuing "backreaction" on the averaged ge...

After recalling a general non-perturbative expression for the luminosity-redshift relation holding in a recently proposed "geodesic light-cone" gauge, we show how it can be transformed to phenomenologically more convenient gauges in which cosmological perturbation theory is better understood. We present, in particular, the complete result on the luminosity-redshift relation in the Poisson gauge up to second order for a fairly generic perturbed cosmology, assuming that appreciable vector and tensor perturbations are only generated at second order. This relation provides a basic ingredient for the computation of the effects of stochastic inhomogeneities on precision dark-energy cosmology whose results we have anticipated in a recent letter. More generally, it can be used in connection with any physical information carried by light-like signals traveling along our past light-cone. 95.36.+x, 98.80.Es 1 Following the pioneering work of [5], d L has been already computed to first order in the longitudinal gauge (for a CDM model in [6], CDM and ΛCDM in [7] and for a generic model in [2]), and to second order in the synchronous gauge, but only for a dust-dominated Universe, in [8]. 2 Except if caustics form. It has been argued [10] that the area distance is modified when caustics are present inside the past light-cone.