Constructing LTB exact solutions in agreement with $H_0$ observations : some tools for exact structure formation and inhomogeneous cosmology

Details Constructing LTB exact solutions in agreement with $H_0$ observations : some tools for exact structure formation and inhomogeneous cosmology Constructing LTB exact solutions in agreement with $H_0$ observations : some tools for exact structure formation and inhomogeneous cosmology

2011-12-08

arxiv.org/abs/1112.1777v1

Astronomy and Astrophysics

Astrophysics

Cosmology and Extragalactic Astrophysics

15 pages

Scientific paper

LTB solutions can have application both in a cosmological and an astrophysical context. They can in fact be used to model large scale inhomogeneities or to study exactly the spherical collapse. We give a general and unified derivation of the analytical solution with and without cosmological constant. A compact anaytical formula is derived which is valid both for positive and negative curvature, allowing to study both expanding an contracting phase without the need to introduce different branches. We then show how to construct solutions in agreement with an arbitrary value of $H_0$. This method can be applied to fully exploit LTB solutions in designing models alternative to dark energy without making any restrictive or implicit assumption about the inhomogeneity profile. In this approach $H_0$ is not a quantity derived from other parameters of the model but rather the fundamental length scale in terms of which any other quantity is defined. The some solution can also be used to study structure formation in the regime in which perturbation theory is not enough and an exact solution of the Einstein's equation is required.

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