# Nonlinear fractal meaning of the Hubble constant

## TL;DR

This paper presents a theoretical fractal model to determine the global Hubble constant without empirical constants, revealing an inverse relationship between measurement accuracy and coordinate calculation precision in cosmology.

## Contribution

It introduces a nonlinear fractal approach to model the universe's expansion and derive the Hubble constant theoretically, avoiding empirical parameters.

## Key findings

- Existence of inverse proportionality between measurement accuracy and coordinate calculation accuracy.
- Theoretical derivation of the Hubble constant without empirical constants.
- Demonstration of ambiguity in cosmological observations due to fractal properties.

## Abstract

According to astrophysical observations value of recession velocity in a certain point is proportional to a distance to this point. The proportionality coefficient is the Hubble constant measured with 5% accuracy. It is used in many cosmological theories describing dark energy, dark matter, baryons, and their relation with the cosmological constant introduced by Einstein. In the present work we have determined a limit value of the global Hubble constant (in a big distance from a point of observations) theoretically without using any empirical constants on the base of our own fractal model used for the description a relation between distance to an observed galaxy and coordinate of its center. The distance has been defined as a nonlinear fractal measure with scale of measurement corresponding to a deviation of the measure from its fixed value (zero-gravity radius). We have suggested a model of specific anisotropic fractal for simulation a radial Universe expansion. Our theoretical results have shown existence of an inverse proportionality between accuracy of determination the Hubble constant and accuracy of calculation a coordinates of galaxies leading to ambiguity results obtained at cosmological observations.

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Source: https://tomesphere.com/paper/1706.04841