Testing backreaction effects with observations

27 pages; new version with a corrected way to compute the redshifts; conclusions remain unchangedInternational audienceIn order to quantitatively test the ability of averaged inhomogeneous cosmologies to correctly describe observations of the large-scale properties of the Universe, we introduce a smoothed template metric corresponding to a constant spatial curvature model at any time, but with an evolving curvature parameter. This metric is used to compute quantities along an approximate effective light cone of the averaged model of the Universe. As opposed to the standard Friedmann model, we parametrize this template metric by exact scaling properties of an averaged inhomogeneous cosmology, and we also motivate this form of the metric by results on a geometrical smoothing of inhomogeneous cosmological hypersurfaces. The purpose of the paper is not to demonstrate that the backreaction effect is actually responsible for the dark energy phenomenon by explicitly calculating the effect from a local model of the geometry and the distribution of matter, but rather to propose a way to deal with observations in the backreaction context, and to understand what kind of generic properties have to hold in order for a backreaction model to explain the observed features of the Universe on large scales. We test our hypothesis for the template metric against supernova data and the position of the cosmic microwave background peaks, and infer the goodness of fit and parameter uncertainties. We find that averaged inhomogeneous models can reproduce the observations without requiring an additional dark energy component (though a volume acceleration is still needed), and that current data do not disfavor our main assumption on the effective light cone structure. We also show that the experimental uncertainties on the angular diameter distance and the Hubble parameter from baryon acoustic oscillations measurements--forseen in future surveys like the proposed EUCLID satellite project--are sufficiently small to distinguish between a Friedmann-Lemaître-Robertson-Walker template geometry and the template geometry with consistently evolving curvature