III. Ecosmos: A Revolutionary Fertile, Habitable, Solar-Bioplanet Incubator Lifescape

E. Systems Cosmology: Fractal SpaceTimeMatter

De la Fuente Marcos, R. and C. Multifractal Evolution in Interacting Galaxies. Monthly Notices of the Royal Astronomical Society. 372/279, 2006. Suffolk University, Madrid campus, astronomers quantify the self-similar geometries that result via celestial confluences from supergiant clouds to stellar superclusters.

Multifractality can be understood as superposition of different fractal patterns. (280)

De Marzo, Giordani, et al. Zipf’s Law for Cosmic Structures. Astronomy & Astrophysics. 651/A114, 2021. The collegial authors, GDM, Francesco Sylos Labini and Luciano Pietronero, Centro Ricerche Enrico Fermi, Rome, have been pioneer researchers of galactic geometries since the early 2000s, as noted in this section. But back then, only initial, spurious inklings could be found. In the two decades since, an actual reality of an innate, harmonic lawfulness across the celestial parsecs has become robustly evident. By this latest posting, into the 2020s an independent, fractal-like self-similarity is considered to take on a distinct textual-like quality. See also Dynamical Approach to Zipf’s Law by this group in Physical Review Research (3/013084, 2021) for a further descriptions, and applications to a far removed urban universe.

The statistical characterization of the distribution of visible matter in the universe is a central problem in modern cosmology. In this respect, a crucial question concerns how large are the greatest structures in the universe. This point is related to whether or not such a distribution can be approximated as being homogeneous on large enough scales. Here we consider the size distribution of superclusters of galaxies and leverage the Zipf-Mandelbrot law to complement an analysis based on correlation functions. We find that galaxy superclusters are described by a pure Zipf's law which implies that the current catalogs are not large enough to spot a truncation in the power-law behavior. (Abstract excerpt)

Exploiting the same methodology we also analyzed the distribution of matter on smaller scales, considering the distribution of clusters rather that that of superclusters. In this case strong deviations from Zipf's law are observed and therefore, on scales of few Mpc, the distribution of matter is self-averaging, confirming previous findings which have also shown this distribution to be fractal on such scales. (6)

De Vega, H., et al. Fractal Structures and Scaling Laws in the Universe. Chaos, Solitons & Fractals. 10/2-3, 1999. More mathematical insights into nature’s iterative geometry.

Fractal structures are observed in the universe in two very different ways. Firstly, in the gas forming the cold interstellar medium in scales from 10-4pc till 100pc. Secondly, the galaxy distribution has been observed to be fractal in scales up to hundreds of Mpc.” (329) (pc = parsecs = 3.26 light years).

Demianski, Marek and Andrei Doroshkevich. Self Similarity of the Dark Matter Dominated Objects and the Shape of Small Scale Power Spectrum. arXiv:1701.03474. A latest posting by University of Warsaw and Lebedev Physical Institute of the Russian Academy of Sciences, senior astrophysicists contributes to global understandings of an iterative cosmic topology and emergence which seems trying to achieve self-recognition through its worldwise human phenomenon.

One of the important goals of cosmology is to establish correlations between the observed Universe – the CMB, Large Scale Structure (LSS), galaxies etc. – and the processes that occurred at the earlier epochs of evolution of the Universe and are encoded in the initial power spectrum of density perturbations. For larger scale D > 10Mpc this problem is approximately solved by the CMB observations of the WMAP missions and is realized as the standard ΛCDM model. However the shape of the power spectrum at small scale remains unknown and its investigation is one of the actual current problem of cosmology. Now it is unfortunately not possible to obtain reliable information about this very important issue. Next very interesting problem is the universality and the self similarity of the internal structure of DM dominated halos in a wide range of their masses and sizes. (1)

Deppman, Airton. Fractal Structure of Hadrons: Experimental and Theoretical Signatures. Universe. Online August, 2017. It is ever amazing that we peoples can proceed altogether to plumb such physical depths and sidereal reaches. Here a University of Sao Paulo astrophysicist advises about an apparent intrinsic propensity of subatomic particles to form self-similar geometries. One then wonders as to where these mathematical lineaments came from, what other reality or persona might have put them there? See also Fractals, Nonextensive Statistics and Quantum Chromodynamics by Airton, Deppman, et al in Physical Review D (101/034019, 2020).

One important ingredient in the study of cosmological evolution is the equation of state of the primordial matter formed in the first stages of the Universe. It is believed that the first matter produced was of hadronic nature, probably the quark–gluon plasma which has been studied in high-energy collisions. There are several experimental indications of self-similarity in hadronic systems—in particular in multiparticle production at high energies. Theoretically, this property was associated with the dynamics of particle production, but it is also possible to relate self-similarity to the hadron structure—in particular to a fractal structure of this system. In the present work, a review of the theoretical developments related to the thermodynamical properties of hadronic matter and its applications in other fields is presented. (Abstract)

Doering, Andreas and Tim Palmer. New Geometric Concepts in the Foundations of Physics. Philosophical Transactions of the Royal Society A. 373/Issue 2047, 2015. The Universitat Erlangen-Nurnberg and Oxford University physicists edit papers from a November 2013 workshop with this title that while admitting LHC Higgs boson and other successes, many problems remain out of reach for current theories. Led by Palmer (search) it is proposed that a more structural, topological approach might help resolve disparate issues. While the meeting included leaders such as Roger Penrose and Gerard ‘t Hooft, the 14 male authors each seemed to have one piece of the puzzle, with few attempts at an integral unity or vision. For example, Xavier Calumet considered a potential energy dependence of Planck’s constant; Cruz Morales and Zilber reformulated quantum mechanics using model theory; Andreas Doering reviewed the topos version of quantum theory; Chris Fewster presents locally covariant quantum field theories; Lucien Hardy proposes quantum theory in terms of bold tensors; Andrew Hodges does twistor geometry; Michael Lapidus presents fractal strings and the Riemann zeta function; Roger Penrose discusses the ‘googly problem’ within twistor cohomology; and Gerard ‘t Hooft (search) presents his programme for a classical, deterministic, real universe underlying quantum systems.

Einasto, Jaan, et al. On Fractal Properties of the Cosmic Web. arXiv:2002.02813. When scientific research began to shift to a worldwide collaboration in the early 2000s, this section could only document sparse inklings of reliable geometric patterns as they suffuse the celestial raiment. Here and now, Tartu Observatory, Estonia astrophysicists quantify in much mathematical detail their presence at every self-similar instance and scale. See also Evolution of Superclusters in the Cosmic Web by this group at 1901.09378. Johannes Kepler and Galileo Galilei would be gratified. Our natural philoSophia view may finally be encountering and verifying the vital, recursive structurations that are there on their intrinsic own.

El Naschie, Mohamed. Fractal Black Holes and Information. Chaos, Solitons and Fractals. 29/1, 2006. The latest theories of the University of Alexandria, Egypt physicist that nature is deeply fractally self-similar in kind from quantum to celestial realms. El Naschie edits this highly technical monthly journal where many of his papers can be found. We are aware that he has been taken to task (2008) over this excess, and plans to resign, but feel this real natural recurrence merits expression.

Elbert, Oliver, et al. Core Formation in Dwarf Haloes with Self-Interacting Dark Matter. Monthly Notices of the Royal Astronomical Society. 453/1, 2015. A team of astrophysicists from UC Irvine, SciTech Analytics, and Ohio State University, including James Bullock conceiver of the theory, explore implications of a novel view of this ambient materiality which serves to fill out the large-scale cosmic structure. Since a static dark matter did not pass tests, Bullock wondered if it might interact with itself in a similar way as ponderable elements and chemicals, which has since gained credence. These inklings of an actively self-constructing universe compose an August 2015 Quanta Magazine article The Case for Complex Dark Matter.

Ettori, Stefano, et al. From Universal Profiles to Universal Scaling Laws in X-ray Galaxy Clusters. arXiv:2010.04192. Two decades into the 21st century, INAF Osservatorio di Astrofisica e Scienza dello Spazio, Bolonga are able to well quantify the “standard self-similar behavior” of celestial spacescapes. Again it amazes that our individual and collective sapience on an infinitesimal bioworld can altogether yet learn about any infinite reach. Wherever did these intrinsic, non-random, geometries that continue in kind to our own selves actually come from?

As end products of the hierarchical process of cosmic structure formation, galaxy clusters present some predictable properties from astrophysical dissipative processes that show remarkable "universal" behaviour once rescaled by halo mass and redshift. However, a consistent picture that links these profiles and the thermodynamic intracluster medium has to be demonstrated. In this work, we use a semi-analytic model based on a "universal" pressure profile in hydrostatic equilibrium within a cold dark matter halo with a defined relation between mass and concentration to reconstruct the scaling laws between the X-ray properties of galaxy clusters. (Abstract)

Feinstein, Adina, et al. Testing Self-Organized Criticality Across the Main Sequence using Stellar Flares from TESS. arXiv:2109.07011.. University of Chicago, MIT and University of Michigan (Fred Adams) add a latest confirmation of nature’s celestial innate preference to reside at this state of optimum efficiency in every disparate instance.

Stars produce explosive flares, which are believed to be powered by the release of energy stored in coronal magnetic field configurations. It has been shown that solar flares exhibit energy distributions typical of self-organized critical systems. This study applies a novel flare detection technique to data obtained by NASA's TESS mission and identifies ∼106 flaring events on ∼105 stars across spectral types. Our results suggest that magnetic reconnection events that maintain the topology of the magnetic field in a self-organized critical state are ubiquitous among stellar coronae. (Abstract)

While the sand pile analogy is simplistic by construction, self-organized criticality naturally manifests in a variety of physical systems. Applications have been found in hydrodynamical turbulence, forest fires and other percolation systems, landslides, neuroscience, climate fluctuations, rainfall, accretion disks, traffic jams, evolution, extinction, financial markets and even Conway's game of Life, to name a non-comprehensive list. (1)

Ferreira, Pedro, et al. Inflation in a Scale Invariant Universe. arXiv:1802.06069. When this section went online in 2004, only inklings of an inherent similarity across the range of celestial phenomena existed. Into the later 2010s, Oxford University, Fermi NAL, and ETH Zurich theorists, as they delve within global collaborations, can now post a theoretical affirmation. This consistent commonality is braced by a dense mathematics as it reveals a natural cosmos suffused, as tradition long intimated, with an infinite repetition in kind across the parsecs and billennia.

A scale-invariant universe can have a period of accelerated expansion at early times: inflation. We use a frame-invariant approach to calculate inflationary observables in a scale invariant theory of gravity involving two scalar fields - the spectral indices, the tensor to scalar ratio, the level of isocurvature modes and non-Gaussianity. We show that scale symmetry leads to an exact cancellation of isocurvature modes and that, in the scale-symmetry broken phase, this theory is well described by a single scalar field theory. We find the predictions of this theory strongly compatible with current observations. (Abstract)

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