Effect of inhomogeneities on the luminosity distance-redshift relation: Is dark energy necessary in a perturbed universe?

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Abstract
The luminosity distance-redshift relation is one of the fundamental tools of modern cosmology. We compute the luminosity distance-redshift relation in a perturbed flat matter-dominated Universe, taking into account the presence of cosmological inhomogeneities up to second order in perturbation theory. Cosmological observations implementing the luminosity distance-redshift relation tell us that the Universe is presently undergoing a phase of accelerated expansion. This seems to call for a mysterious Dark Energy component with negative pressure. Our findings suggest that the need of a Dark Energy fluid may be challenged once a realistic inhomogeneous Universe is considered and that an accelerated expansion may be consistent with a matter-dominated Universe.