Galaxy distributions as fractal systems

Abstract

This paper discusses if large scale galaxy distribution samples containing almost one million objects can be characterized as fractal systems. The analysis performed by Teles et al. (Phys Lett B 813:136034, 2021) on the UltraVISTA DR1 survey is extended here to the SPLASH and COSMOS2015 catalogs, hence adding 750k new galaxies with measured redshifts to the studied samples. The standard $$\Lambda $$ Λ CDM cosmology having $$H_0=(70\pm 5)$$ H 0 = ( 70 ± 5 ) km/s/Mpc and number density tools required for describing these galaxy distributions as single fractal systems with dimension D are adopted. We use the luminosity distance $$d_{\scriptscriptstyle L}$$ d L , redshift distance $$d_z$$ d z and galaxy area distance (transverse comoving distance) $$d_{\scriptscriptstyle G}$$ d G as relativistic distance definitions to derive galaxy number densities in the redshift interval $$0.1\le z\le 4$$ 0.1 ≤ z ≤ 4 at volume limited subsamples defined by absolute magnitudes in the K-band. Similar to the findings of Teles et al. (2021), the results show two consecutive redshift scales where galaxy distribution data behave as single fractal structures. For $$z<1$$ z < 1 we found $$D=1.00\pm 0.12$$ D = 1.00 ± 0.12 for the SPLASH galaxies, and $$D=1,39\pm 0.19$$ D = 1 , 39 ± 0.19 for the COSMOS2015. For $$1\le z\le 4$$ 1 ≤ z ≤ 4 we respectively found $$D=0.83^{+0.36}_{-0.37}$$ D = 0 . 83 - 0.37 + 0.36 and $$D=0.54^{+0.27}_{-0.26}$$ D = 0 . 54 - 0.26 + 0.27 . These results were verified to be robust under the assumed Hubble constant uncertainty. Calculations considering blue and red galaxies subsamples in both surveys showed that the fractal dimensions of blue galaxies as basically unchanged, but the ones for the red galaxies changed mostly to smaller values, meaning that D may be seen as a more intrinsic property of the distribution of objects in the Universe, therefore allowing for the fractal dimension to be used as a tool to study different populations of galaxies. All results confirm the decades old theoretical prediction of a decrease in the fractal dimension for $$z>1$$ z > 1 .

Elliptical Space with the McVittie Metrics

“…In these models, matter clumping was found to be fractal [21,22], which is confirmed by statistical studies of CMBR maps [20] and of the matter distribution in the Universe [17][18][19]. By contrast, according to the ΛCDM scenario, matter distribution cannot be fractal.…”

“…Therefore, the luminosity distance ( 18) and ( 19), which is given in units of r g , can be used for the McVittie metric case, if one takes care of the time-dependent distance unit (23). The time t in ( 21) can be calculated, to the first approximation, by using the static distance d L divided by the speed of light (c = 1 in units of r g ) with the first correcting sub-factor in (19) removed, because the loss of luminosity due to the cosmological redshift z is not applied when calculating the light-travel distance. That is,…”

“…In terms of frequencies, H = 2.146 • 10 −20 [s −1 ], which constrains the age of the Universe to H −1 = 4.66 • 10 19 [s] or…”

“…For example, the perturbative approach used in ΛCDM to explain the structureformation in the Universe is challenged by the fact that on scales below 100 Mpc the matter distribution in the Universe is extremely inhomogeneous, which is also related to some other issues with ΛCDM [16]. Statistical studies of matter distribution [17][18][19] and of the CMBR [20] indicate that the Universe is fractal, which is in line with earlier theoretical studies of static cosmological models [21,22]. According to the ΛCDM scenario, fractal distribution of matter is impossible.…”

Constant Acceleration in Fractal Structures with Fractal Dimension D = 2

“…A reduced UltraVISTA survey subsample containing 166,566 galaxies was used in this study. Teles et al (2022) extended the previous data sample by adding 750 k new galaxies with measured redshifts using SPLASH and COSMOS2015 catalogues. A decrease in the fractal dimension for a redshift z > 1 was confirmed.…”