Single Past Null Geodesic in the Lemaitre-Tolman-Bondi Cosmology

Understand

This work provides a general discussion of the spatially inhomogeneous Lema\^itre-Tolman-Bondi (LTB) cosmology, as well as its basic properties and many useful relevant quantities, such as the cosmological distances.

• We apply the concept of the single null geodesic to produce some simple analytical solutions for observational quantities such as the redshift.
• As an application of the single null geodesic technique, we carry out a fractal approach to the parabolic LTB model, comparing it to the spatially homogeneous Einstein-de Sitter cosmology.
• The results obtained indicate that the standard model, in this case represented by the Einstein-de Sitter cosmology, can be equivalently described by a fractal distribution of matter, as we found that different single fractal dimensions describe different scale ranges of the parabolic LTB matter distribution.