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Register a new userFractal universe and cosmic acceleration in a Lema^itre-Tolman-Bondi scenario
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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 Lema^itre-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 $D=2.9 pm 0.02$.
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We provide a formula for estimating the redshift and its secular change (redshift drift) in Lema^itre-Tolman-Bondi (LTB) spherically symmetric universes. We compute the scaling of the redshift drift for LTB models that predict Hubble diagrams indistinguishable from those of the standard cosmological model, the flat $Lambda$ Cold Dark Matter ($Lambda$CDM) model. We show that the redshift drift for these degenerate LTB models is typically different from that predicted in the $Lambda$CDM scenario. We also highlight and discuss some unconventional redshift-drift signals that arise in LTB universes and give them distinctive features compared to the standard model. We argue that the redshift drift is a metric observable that allows to reduce the degrees of freedom of spherically symmetric models and to make them more predictive and thus falsifiable.
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