Observational constraints on inhomogeneous cosmological models without dark energy

It has been proposed that the observed dark energy can be explained away by the effect of large-scale nonlinear inhomogeneities. In the present paper we discuss how observations constrain cosmological models featuring large voids. We start by considering Copernican models, in which the observer is not occupying a special position and homogeneity is preserved on a very large scale. We show how these models, at least in their current realizations, are constrained to give small, but perhaps not negligible in certain contexts, corrections to the cosmological observables. We then examine non-Copernican models, in which the observer is close to the center of a very large void. These models can give large corrections to the observables which mimic an accelerated FLRW model. We carefully discuss the main observables and tests able to exclude them.Comment: 27 pages, 7 figures; invited contribution to CQG special issue "Inhomogeneous Cosmological Models and Averaging in Cosmology". Replaced to match the improved version accepted for publication. Appendix B and references adde

How does the cosmic large-scale structure bias the Hubble diagram?

The Hubble diagram is one of the cornerstones of observational cosmology. It is usually analysed assuming that, on average, the underlying relation between magnitude and redshift matches the prediction of a Friedmann-Lema\^itre-Robertson-Walker model. However, the inhomogeneity of the Universe generically biases these observables, mainly due to peculiar velocities and gravitational lensing, in a way that depends on the notion of average used in theoretical calculations. In this article, we carefully derive the notion of average which corresponds to the observation of the Hubble diagram. We then calculate its bias at second-order in cosmological perturbations, and estimate the consequences on the inference of cosmological parameters, for various current and future surveys. We find that this bias deeply affects direct estimations of the evolution of the dark-energy equation of state. However, errors in the standard inference of cosmological parameters remain smaller than observational uncertainties, even though they reach percent level on some parameters; they reduce to sub-percent level if an optimal distance indicator is used.Comment: 19+7 pages, 10 figures, v2 accepted by JCAP; minor changes to improve clarit