Can the cosmological constant be mimicked by smooth large-scale inhomogeneities for more than one observable?

Details Can the cosmological constant be mimicked by smooth large-scale inhomogeneities for more than one observable? Can the cosmological constant be mimicked by smooth large-scale inhomogeneities for more than one observable?

2009-12-15

arxiv.org/abs/0912.2866v3

JCAP05(2010)020

Astronomy and Astrophysics

Astrophysics

Cosmology and Extragalactic Astrophysics

18 pages, corrected a typo in the definition of the energy density which doesn't change the conclusion, references added

Scientific paper

10.1088/1475-7516/2010/05/020

As an alternative to dark energy 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. In order to test such an hypothesis we calculate the low redshift expansion of the luminosity distance $D_L(z)$ and the redshift spherical shell mass density $mn(z)$ for a central observer in a LTB space without cosmological constant and show how they cannot fit the observations implied by a $\Lambda CDM $ model if the conditions to avoid a weak central singularity are imposed, i.e. if the matter distribution is smooth everywhere. Our conclusions are valid for any value of the cosmological constant, not only for $\Omega_{\Lambda}>1/3$ as implied by previous proofs that $q^{app}_0$ has to be positive in a smooth LTB space, based on considering only the luminosity distance. The observational signatures of smooth LTB matter dominated models are fundamentally different from the ones of $\Lambda CDM $ models not only because it is not possible to reproduce a negative apparent central deceleration $q^{app}_0$, but because of deeper differences in their space-time geometry which make impossible the inversion problem when more than one observable is considered, and emerge at any redshift, not only for $z=0$.

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