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Spatial averaging and apparent acceleration in inhomogeneous spaces

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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.

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Authors and Affiliations

  1. Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto, 606-8502, Japan

    Antonio Enea Romano & Misao Sasaki

  2. Leung Center for Cosmology and Particle Astrophysics, National Taiwan University, Taipei, 10617, Taiwan, ROC

    Antonio Enea Romano

  3. Instituto de Fisica, Universidad de Antioquia, A.A.1226, Medellin, Colombia

    Antonio Enea Romano

Authors
  1. Antonio Enea Romano
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  2. Misao Sasaki
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Correspondence to Antonio Enea Romano.

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Romano, A.E., Sasaki, M. Spatial averaging and apparent acceleration in inhomogeneous spaces. Gen Relativ Gravit 44, 353–365 (2012). https://doi.org/10.1007/s10714-011-1277-4

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  • DOI: https://doi.org/10.1007/s10714-011-1277-4

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