Observational constraints on the fractal cosmology

TL;DR

This study investigates a fractal universe model's implications for cosmic structure and expansion, finding it inconsistent with some observations and tightly constrained by data, thus aligning closely with standard cosmology.

Contribution

It derives and tests a fractal cosmology model against observational data, providing the first comprehensive constraints on its parameters and assessing its viability.

Findings

Higher structure growth in fractal cosmology contrasts with galaxy surveys.

Hubble constant decreases in fractal models, conflicting with low-redshift measurements.

Constraints show no significant deviation from standard cosmology.

Abstract

In this paper, we explore a fractal model of the universe proposed by Calcagni [JHEP{\bf03}(2010)120] for a power-counting renormalizable field theory living in a fractal spacetime. Considering a timelike fractal profile, we derived field equations in fractal cosmology, in order to explore the structure formation and the expansion history in fractal universe. Numerical investigations based on matter power spectra diagrams report higher structure growth in fractal cosmology, being in contrast to local galaxy surveys. Additionally, according to the evolution of Hubble parameter diagrams, it can be understood that Hubble constant would decrease in fractal cosmology, which is also incompatible with low redshift estimations of $H_0$. So, concerning primary numerical studies, it seems that fractal cosmology is not capable to alleviate the tensions between local and global observational probes. Then, in pursuance of more accurate results, we constrain the fractal cosmology by observational data, including Planck cosmic microwave background (CMB), weak lensing, supernovae, baryon acoustic oscillations (BAO), and redshift-space distortions (RSD) data. The derived constraints on fractal dimension $\beta$ indicate that there is no considerable deviation from standard model of cosmology.