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

E. Systems Cosmology: Fractal SpaceTimeMatter

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)

Fiete, Gregory and Alex de Lozanne. Seeing Quantum Fractals. Science. 327/652, 2010. University of Texas physicists use scanning, tunneling microscopy to discern indications of fractal forms in electronic structures of a magnetic Gallium Arsenide semiconductor, along with novel signs of a self-organized quantum criticality. (see also arXiv:0910.1338)

Fractals actually abound in nature: Galaxies, clouds, mountains, trees, and broccoli are all familiar examples. But fractals can occur in the quantum realm as well, even though they have never been observed, until, perhaps, now. (652)

Figueroa, Daniel, et al. Exact Scale-Invariant Background of Gravitational Waves from Cosmic Defects. Physics Review Letters. 110/101302, 2013. University of Geneva, University of Helsinki, and University of the Basque Country astrophysicists contribute instrumental and mathematical findings of self-ordering celestial processes across the parsecs as they array into nested stratifications which repeat the same phenomena everywhere. With such a scenario, one wonders what kind of universe is able to achieve, billions of years on, on a minute bioplanet, a modicum of its own self-witness, decipherment and description. For whatever purpose might we at some point ask about and awaken to?

We demonstrate that any scaling source in the radiation era produces a background of gravitational waves with an exact scale-invariant power spectrum. Cosmic defects, created after a phase transition in the early universe, are such a scaling source. We emphasize that the result is independent of the topology of the cosmic defects, the order of phase transition, and the nature of the symmetry broken, global or gauged. As an example, using large-scale numerical simulations, we calculate the scale-invariant gravitational wave power spectrum generated by the dynamics of a global O(N) scalar theory. (Abstract)

Fratini, Michela, et al. Scale-free Structural Organization of Oxygen Interstitials in La2CuO4+y.. Nature. 466/481, 2010. Italian and French physicists are able to detect pervasive nonlinear network geometries within this candidate superconducting material. Their innate, spontaneous presence might then be taken to suggest an independent, universal mathematical source.

It is also known that complex systems often have a scale-invariant structural organization, but hitherto none had been found in high-Tc materials. Here we report that the ordering of oxygen interstitials in the La2O2+y spacer layers of La2CuO4+y high-Tc superconductors is characterized by a fractal distribution up to a maximum limiting size of 400 μm. Intriguingly, these fractal distributions of dopants seem to enhance superconductivity at high temperature. (481)

The data also raise the more intriguing question of whether the oxygen defects order on fractal networks because the electrons that form the strange metal constitute a ‘fractal glue,’ perhaps generated as a photographic-like image of the quantum critical charge fluctuations sampled during annealing (at temperatures well within the non-Fermi-liquid regime). (483)

Fujiwara, Noboru. The Scaling Rule for Environmental Organizing Systems in a Gravitational Field. BioSystems. 73/2, 2004. A computer scientist at the Nara Women’s University in Japan finds a constant, proportional relationship from unicellular organisms to humans and on to stellar dimensions. As cosmic and planetary evolution proceeds, it can be qualified by an increase in organized information. Fujiwara’s studies have been periodically published in this journal.

The present paper examines a scaling rule for the relationship between the integrated scaled metabolic energy and the mass of a system for a wide range of masses, from animals to 4He cores of main-sequence stars, considering the effect of gravitational energy. (111)

Furtenbacher, Tibor, et al. Simple Molecules as Complex Systems. Nature Scientific Reports. 4/4654, 2014. Hungarian and German chemists, mathematicians, and physicists broach how ubiquitous network phenomena can be extrapolated even to quantum activities. In regard, one lively universe to us, cosmic to civic, similar anatomy and physiology is being deftly filled in. However in this month of May might it dawn that our planetary progeny is discovering a grand new genesis

For individual molecules, quantum mechanics (QM) offers a simple, natural and elegant way to build large-scale complex networks: quantized energy levels are the nodes, allowed transitions among the levels are the links, and transition intensities supply the weights. QM networks are intrinsic properties of molecules and they are characterized experimentally via spectroscopy; thus, realizations of QM networks are called spectroscopic networks (SN). The proposed novel view of high-resolution spectroscopy and the observed degree distributions have important implications: appearance of a core of highly interconnected hubs among the nodes, a generally disassortative connection preference, considerable robustness and error tolerance, and an “ultra-small-world” property. The network-theoretical view of spectroscopy offers a data reduction facility via a minimum-weight spanning tree approach, which can assist high-resolution spectroscopists to improve the efficiency of the assignment of their measured spectra. (Abstract)

Gaite, Jose. Scale Symmetry in the Universe. Symmetry. 12/4, 2020. As noted herein, when this section went online in 2004 only patchy inklings of self-similar cosmic structures could be found. In this essay a Polytechnic University of Madrid physicist (search) can well quantify and install a “multifractal cosmology” in extensive mathematical detail. The celestial reaches which firstly seem vastly opaque are now found to be suffused with a discernible patterning due an infinity of nested repetitions. The atomic quantum depths are likewise graced by a fractal fabric, along with the mesocosmic phases in between. Circa 2020, as a worldwise supermind proceeds to learns by itself, the ancient, tradition sense of an as above, so below correspondence is at last becomes verified and explained.

Scale symmetry is a fundamental symmetry of physics that seems however not to be fully realized in the universe. Here, we focus on the astronomical scales ruled by gravity, where scale symmetry holds and gives rise to a scale invariant distribution of matter, namely a true fractal geometry. A suitable explanation of the fractal cosmic mass distribution is provided by the nonlinear Poisson–Boltzmann–Emden equation. We study the fractal solutions of the equation and connect them with the statistical theory of random multiplicative cascades. The type of multifractal mass distributions so obtained agrees with results from the analysis of cosmological simulations and of observations of the galaxy distribution. (Abstract)

Simply put, if one finds an object of a given size, there must be similar objects of larger size. For example, take a cluster of galaxies; there must be similar superclusters of every possible size. Not surprisingly, the idea of a scale invariant structure of the universe on large scales is old, but its modern formulation had to await the advent of the appropriate description in the form of fractal geometry. Simple fractals are scale invariant and are indeed composed of clusters of clusters of down to the infinitesimally small. Naturally, in the universe, the self-similarity must stop at a scale about the size of galaxies, although it could be limitless towards the large scales, in principle. (1-2)

Gefter, Amanda. Fractal Universe. New Scientist. March 10, 2007. To the proponents of this vision such as Luciano Pietronero of the University of Rome, the latest results of the Sloan Digital Sky Survey of over 50,000 galaxies quite support a self-similar geometry across many scales. But from another mathematical approach, David Hogg of New York University finds a homogeneity across their span of 400 million light years. His worry is that relativistic physics would be in peril because it cannot explain how these iterative structures would arise. (An interesting note is included about initial indications that dark matter, which makes up some 85% of the cosmos, also appears to take on a fractal array.) These discussions reflect an inability of the 20th century particulate emphasis, albeit a necessary stage, to appreciate complex, self-organizing phenomena because they lie outside their model and survey.

Grudic, Michael and Philip Hopkins. The Opacity Limit. arxiv:2308.16268. As Carnegie Observatories and CalTecn astronomers describe a dense theoretical finesse, they also provide another vivid affirmation which stands as an seamless extension of nature's univeral scalar geometries. With Miguel Aragon-Calvo, et al, the early inklings of the 2000s by now stretch wide and deep across the celestial raiment, as a major Earthwise vista.

The opacity limit is an important concept in star formation: isothermal collapse cannot proceed without limit, because eventually cooling radiation is trapped and the temperature rises quasi-adiabatically, setting a minimum Jeans mass. We derive expressions for the thermal evolution of dust-cooled collapsing gas clumps in various limiting cases, and a general power-law dust opacity law. (Excerpt)

We live in a hierarchical universe, consisting of nestedstructures spanning a vast range of scales from the cosmic web down to to moons and asteroids. It is natural for inhabitants of such a universe to ask: where does structure formation stop? Gravity is scale-free but other processes are not, so surely at times the laws of physics must step in and say no more, preventing some structures from spawning substructures. (1)

Guszejnov, David, et al. Universal Scaling Relations in Scale-Free Structure Formation. arXiv:1707.05799. Reviewed more in Mid 2010s Universality, whereof a sophisticated cosmic science by Cal Tech astrophysicists affirms a pervasive, natural interstellar self-similarity.

Halasz, Gabor, et al. Fracton Topological Phases from Strongly Coupled Spin Chains. arXiv:1707.02308. UC Santa Barbara, Kavli Institute, theorists press this intricate mathematical discernment of quantum structures. We quote the opening paragraph as to convey this initial phase of mapping a frontier expanse which is just opening. See also, e.g., Fracton Models on General Three-Dimensional Manifolds at 1712.05892 for more exposition.

Fracton topological phases are topologically ordered phases in three dimensions with a particularly extreme form of fractionalization. In these phases, there are point-like excitations that are either completely immobile or only mobile in a lower-dimensional subsystem, such as an appropriate line or plane. Remarkably, the restricted mobility of excitations has a purely topological origin and appears in translation-invariant systems without any disorder. In addition to being of fundamental interest from the perspective of topological phases, and providing an exciting disorder-free alternative to many-body localization, this phenomenology has important implications for quantum-information storage. Indeed, the immobility of excitations makes encoded quantum information more stable at finite temperature than in conventional topologically ordered phases. (1)

Hnat, Bogdan, et al. Scale-Free Texture of the Fast Solar Wind. Physical Review E. 84/065401, 2011. University of Warwick, Coventry, Ilia State University, Tbilisi, and Imperial College, London, astrophysicists further quantify the nebulous realms of stellar fractal galaxies. See also “On the Fractal Nature of the Magnetic Field Energy Density in the Solar Wind” in Geophysical Research Letters (34/L15108, 2007).

The higher-order statistics of magnetic field magnitude fluctuations in the fast quiet solar wind are quantified systematically, scale by scale. We find a single global non-Gaussian scale-free behavior from minutes to over 5 h. This spans the signature of an inertial range of magnetohydrodynamic turbulence and a ~ 1/f range in magnetic field components. This global scaling in field magnitude fluctuations is an intrinsic component of the underlying texture of the solar wind and puts a strong constraint on any theory of solar corona and the heliosphere. Intriguingly, the magnetic field and velocity components show scale-dependent dynamic alignment outside of the inertial range. (065401)

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