Fractal cosmology

Fractal cosmology - ideas and theories of physical cosmology , suggesting the infinity of the space of the universe and the distribution of astronomical objects in it according to the principle of self-similar structures ( fractals ). Fractal cosmology denies the spatial homogeneity of the Universe on a large scale and suggests the presence of a fractal dimension (less than 3 ) - a number that determines the distribution of mass . It is the mass contained in the ball centered in the averaged astronomical object that must obey a power law with respect to the radius. In the 21st century, the ideas of fractal cosmology do not enjoy the substantial support of academic science , although the application of fractal theory to cosmology remains the subject of theoretical research.

Content

Background

The development of fractal cosmology was an extrapolation of the hierarchy of the Universe assumed by some 19th-century astronomers ( planets → planet / star systems → “star islands” → ...), which later became a scientifically recognized fact. However, back in 1761, when nothing was known about the existence of other galaxies, the German scientist Johann Lambert published Cosmological Letters on the Structure of the Universe, where he suggested that the Universe is hierarchically and on a large scale: each star with planets forms a first-level system , then these stars are combined into a second-level system, etc. Physical considerations also found that two paradoxes contradict the assumption of an (average) uniform distribution of stars in the Universe: the photometric paradox (Olbers) and the gravitational paradox .

In 1908, Karl Charlier based on the idea of Lambert ^[1] published a theory of the structure of the Universe, according to which the Universe is an infinite collection of systems of each other of ever increasing complexity. In this theory, individual stars form a first-order galaxy, a collection of first-order galaxies forms a second-order galaxy, and so on to infinity. Based on this idea of the structure of the Universe, Charlier came to the conclusion that in the infinite Universe, the photometric and gravitational paradoxes are eliminated if the distances between peer systems are sufficiently large compared to their sizes. Let be $R_{k}$ ${\ displaystyle R_ {k}}$ - average radius of the system $k$ ${\ displaystyle k}$ level and $N_{k}$ ${\ displaystyle N_ {k}}$ - the average number of elements of the previous level that make up the system $k$ ${\ displaystyle k}$ level. Then, as Charlier showed, to eliminate the paradoxes, it suffices to assume that for all levels ^[2] :

{\frac {R_{k}}{R_{k-1}}}>{\sqrt {N_{k}}}.

{\ displaystyle {\ frac {R_ {k}} {R_ {k-1}}}> {\ sqrt {N_ {k}}}.}

If we assume that the fractal dimension of the Universe is the same for all levels, then it should not exceed 2 .

This leads to a continuous decrease in the average density of cosmic matter with the transition to higher-order systems. To eliminate the paradoxes, it is required that the density of the substance fall faster than inversely with the square of the distance from the observer.

However, with the development of the theory of the expanding Universe and, in particular, the General Theory of Relativity , these paradoxes were removed in a different way.

Disclaimers

The dependence of the mass (or the number of galaxies) on the ball radius in the observable Universe , prescribed by the Lambert – Charlier fractal cosmology, is not traced, nor are structures larger than the supercluster of galaxies determined. ^[2] ^[3] Moreover, accurate measurements of the relict microwave radiation intensity carried out in the 21st century show small fluctuations in the gravitational potential in the visible universe, which contradicts the fractal model (in any case, under the assumption of an expanding Universe, described according to GR).

Fractal cosmology in the understanding of Lambert-Charlier also contradicts the cosmological principle .

Modern Development

In 2002, Russian astrophysicist Yuri Baryshev published the book Discovery of Cosmic Fractals , which contains an overview of the ideas of fractal cosmology.

The existence of large groups of quasars is considered by some scientists as a refutation of the uniform distribution of mass in the Universe.

Notes

↑ Carl Ludwig Charlier. Charlier Hierarchy
↑ ¹ ² Relativistic astronomy, 1989 , p. 43 ..
↑ Tegmark et al. The Three-Dimensional Power Spectrum of Galaxies from the Sloan Digital Sky Survey // The Astrophysical Journal : journal. - IOP Publishing 2004 .-- 10 May ( vol. 606 , no. 2 ). - P. 702-740 . - DOI : 10.1086 / 382125 . - . - arXiv : astro-ph / 0310725 .

Literature

Klimishin I. A. Relativistic astronomy. 2nd ed. - M .: Nauka , 1989 .-- 287 p. - (Problems of science and technological progress). - ISBN 5-02-014074-0 . - S. 41–46.

Links

Cosmological picture of the world, resulting from the hypothesis of a fractal universe

[1] Carl Ludwig Charlier. Charlier Hierarchy

[KLIM43-2] ¹ ² Relativistic astronomy, 1989 , p. 43 ..

[Tegmark-3] Tegmark et al. The Three-Dimensional Power Spectrum of Galaxies from the Sloan Digital Sky Survey // The Astrophysical Journal : journal. - IOP Publishing 2004 .-- 10 May ( vol. 606 , no. 2 ). - P. 702-740 . - DOI : 10.1086 / 382125 . - . - arXiv : astro-ph / 0310725 .