Astronomy and Astrophysics – Astrophysics – Cosmology and Extragalactic Astrophysics
Scientific paper
2009-05-20
Astronomy and Astrophysics
Astrophysics
Cosmology and Extragalactic Astrophysics
16 pages, 12 figures. Explicit derivation of the fully analytical null geodesic equations has been added. Published in GRG
Scientific paper
10.1007/s10714-011-1277-4
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 $a^{FLRW}$.
Enea Romano Antonio
Sasaki Misao
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