Fractal universe and cosmic acceleration in a Lemaître-Tolman-Bondi scenario

Abstract

In this paper we attempt to answer to the question: can cosmic acceleration of the Universe have a fractal solution? We give an exact solution of a Lemaître-Tolman-Bondi (LTB) Universe based on the assumption that such a smooth metric is able to describe, on average, a fractal distribution of matter. While the LTB model has a center, we speculate that, when the fractal dimension is not very different from the space dimension, this metric applies to any point of the fractal structure when chosen as center so that, on average, there is not any special point or direction. We examine the observed magnitude-redshift relation of type Ia supernovae (SNe Ia), showing that the apparent acceleration of the cosmic expansion can be explained as a consequence of the fractal distribution of matter when the corresponding space-time metric is modeled as a smooth LTB one and if the fractal dimension on scales of a few hundreds Mpc is $D=2.9\pm 0.02$.

6 pages, 4 figures, accepted for publication in Classical and Quantum Gravity

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• The Scale of Homogeneity in the $R_h=ct$ Universe
• Approximations for the divergence of the local large-scale structure velocity field and its implications for Tilted Cosmology
• Fake dark matter from retarded distortions
• Local Peculiar Motions in McVittie and LTB Spacetimes
• Signature of $f\left(R\right)$ gravity via Lemaître-Tolman-Bondi inhomogeneous perturbations
• A fractal LTB model cannot explain Dark Energy
• Inflation and Primordial Perturbations in Fractal Cosmology
• Large scale structures: from inflation to today: a brief report
• A Quantitative Framework for Testing the Hubble Tension in a Bianchi Type I Cosmological Background
• Galaxy Mergers in a Fractal Cosmology
• On Generalized Lemaitre-Tolman-Bondi Metric. Fractal Matter at the end of Matter-Antimatter Recombination