The Effect of Inhomogeneities on the Luminosity Distance–Redshift Relation: is Dark Energy Necessary in a Perturbed Universe?

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.