Spatial averaging and apparent acceleration in inhomogeneous spaces

Abstract

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. We provide examples of LTB models with positive $a_D$ which fail to reproduce the observed luminosity distance $D_L(z)$. Since the apparent cosmic acceleration $a^{FLRW}$ is obtained from fitting the observed luminosity distance to a FLRW model we conclude that in general a positive $a_D$ in LTB models does not imply a positive $a^{FLRW}$.

16 pages, 12 figures. Explicit derivation of the fully analytical null geodesic equations has been added. Published in GRG

References in corpus (7)

• An inhomogeneous alternative to dark energy?
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• Apparent and average acceleration of the Universe
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• Reconstructing the metric of the local Universe from number counts observations
• Low red-shift effects of local structure on the Hubble parameter in presence of a cosmological constant
• Can smooth LTB models mimicking the cosmological constant for the luminosity distance also satisfy the age constraint?
• Coordinate independent approach to the calculation of the effects of local structure on the luminosity distance
• Relations between physical observables: what is better?
• Nonlinear phenomena in general relativity