Spatial averaging and apparent acceleration in inhomogeneous spaces |
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Authors: | Antonio Enea Romano Misao Sasaki |
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Institution: | 1. Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto, 606-8502, Japan 2. Leung Center for Cosmology and Particle Astrophysics, National Taiwan University, Taipei, 10617, Taiwan, ROC 3. Instituto de Fisica, Universidad de Antioquia, A.A.1226, Medellin, Colombia
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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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Keywords: | |
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