Do recent accurate measurements of $H_0$ really rule out void models as alternatives to dark energy?

Details Do recent accurate measurements of $H_0$ really rule out void models as alternatives to dark energy? Do recent accurate measurements of $H_0$ really rule out void models as alternatives to dark energy?

2011-05-10

arxiv.org/abs/1105.1864v3

Astronomy and Astrophysics

Astrophysics

Cosmology and Extragalactic Astrophysics

19 pages, 3 tables, section added about central smoothness and analysis of the possible solutions of the inversion problem. ar

Scientific paper

Recent accurate measurements of $H_0$ have been claimed to be enough to rule out void models as alternatives to dark energy. Using a local redshift expansion for the luminosity distance and the constraint from the age of the Universe we show that the parameters defining a general LTB model give enough freedom to be in agreement with any value of $H_0$. The proof is based on using $H_0$ as the fundamental length scale in terms of which to express al the other relevant quantities determining the geometry of a LTB metric. We also generalize the notion of central smoothness, corresponding to the requirement that all the odd derivatives of the functions of the radial coordinates defining the model should vanish at the center; without this smoothness condition even derivatives of the energy density would diverge at the center. We consider general LTB models and discuss in details the existence, uniqueness and degeneracy of the solution of the inversion problem consisting in matching the observations of the luminosity distance, $H_0$ and the age of the Universe, classifying models according to the central smoothness and the presence of an isotropic but inhomogeneous big bang. Not surprisingly, given the presence of two free functions to determine a LTB model, we find that solutions to the IP exist both in the smooth and not smooth case. Based on this we argue that before LTB solutions can be conclusively ruled out as viable cosmological models it is important to prescribe a general procedure to design them, not limited by any special assumption for the choice of the parameters necessary to define their geometry or functional ansatz for the shape of the inhomogeneity profile.

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