Spatial averaging and apparent acceleration in inhomogeneous spaces

Understand

As an alternative to dark energy that explains the observed acceleration of the universe, it has been suggested that we may be at the center of an inhomogeneous isotropic universe described by a Lemaitre-Tolman-Bondi (LTB) solution of Einstein's field equations.

• To test this possibility, it is necessary to solve the null geodesics.
• In this paper we first give a detailed derivation of a fully analytical set of differential equations for the radial null geodesics as functions of the redshift in LTB models.
• As an application we use these equaions to show that a positive averaged acceleration $a_D$ obtained in LTB models through spatial averaging can be incompatible with cosmological observations.