
III. Ecosmos: A Revolutionary Fertile, Habitable, SolarBioplanet, Incubator LifescapeE. Systems Cosmology: Fractal SpaceTimeMatter Binggeli, Bruno and Tatjana Hascher. Is There a Universal Mass Function? Publications of the Astronomical Society of the Pacific. 119/592, 2007. Astronomers at the University of Basel report a scaleinvariant universality which holds across all realms of celestial objects as evidence for a common mechanism of star formation. See also Elmegreen in this section for similar findings. In conclusion, the title question of this paper can certainly be answered “yes.” There is a universal mass function in the sense that it is possible to put together a continuous mass function “of the universe” from asteroids and planets, over stars and stellar remnants, star clusters and gas clouds, and galaxies, all the way up to the richest clusters of galaxies. (604) Calcagni, Gianluca. Fractal Universe and Quantum Gravity. Physics Review Letters. 104/251301, 2010. A prominent paper from the Max Planck Institute for Gravitational Physics researcher about his interpretations of natural selfsimilar geometries from quanta to cosmos. More contributions can be viewed on arXiv, such as “Diffusion in Multifractal Spacetime,” published in Physical Review E (Online January 2013). An Abstract from another paper is posted below. We propose a field theory which lives in fractal spacetime and is argued to be Lorentz invariant, powercounting renormalizable, ultraviolet finite, and causal. The system flows from an ultraviolet fixed point, where spacetime has Hausdorff dimension 2, to an infrared limit coinciding with a standard fourdimensional field theory. Classically, the fractal world where fields live exchanges energy momentum with the bulk with integer topological dimension. However, the total energy momentum is conserved. We consider the dynamics and the propagator of a scalar field. Implications for quantum gravity, cosmology, and the cosmological constant are discussed. (Abstract) Capolupo, Antonio, et al. Thermal Condensate Structure and Cosmological Energy Density of the Universe. arXiv:1602.07684. University of Salerno astrophysicists including Giuseppe Vitiello report from our intelligent personsphere that these celestial reaches are quite graced by invariant fractal topologies. The aim of this paper is the study of thermal vacuum condensate for scalar and fermion fields. We analyze the thermal states at the temperature of the cosmic microwave background (CMB) and we show that the vacuum expectation value of the energy momentum tensor density of photon fields reproduces the energy density and pressure of the CMB. We perform the computations in the formal framework of the thermo field dynamics. We also consider the case of neutrinos and thermal states at the temperature of the neutrino cosmic background. Consistency with the estimated lower bound of the sum of the active neutrino masses is verified. In the boson sector, non trivial contribution to the energy of the universe is given by particles of masses of the order of 10−4eV compatible with the ones of the axionlike particles. The fractal selfsimilar structure of the thermal radiation is also discussed and related to the coherent structure of the thermal vacuum. (Abstract) Caputi, Karina. A Generalized PowerLaw Diagnostic for Infrared Galaxies at z>1: Active Galactic Nuclei and Hot Interstellar Dust. Astrophysical Journal. 768/2, 2013. We select this paper from many in these international journals that continue more often to quantify the universal nonlinearity of dynamic celestial nature. As the technical quote attests, a University of Groningen, Kapteyn Astronomical Institute, ArgentineDutch researcher finds a powerlaw scale invariance to take manifest form everywhere. See then in this issue “Cosmic Emulation: The ConcentrationMass Relation for wCDM Universes” by Juliana Kwan, et al. One can also view, for example, the Max Planck Institute for Astronomy website for similar sidereal exemplars. But may we wonder, Whom over the Earth is carrying out this collaborative project of cosmic proportions from instrumental telescopes and satellites to computational and mathematical analysis? The work goes forward, this is not their charge, yet without a natural philosophy guidance as to who we actually might be, why is our minute ovular orb suddenly able to gain such knowledge. I present a generalized powerlaw (PL) diagnostic which allows one to identify the presence of active galactic nuclei (AGNs) in infrared (IR) galaxies at z > 1, down to flux densities at which the extragalactic IR background is mostly resolved. I derive this diagnostic from the analysis of 174 galaxies with S ν(24 μm)>80 μJy and spectroscopic redshifts z spec > 1 in the Chandra Deep Field South, for which I study the restframe UV/optical/nearIR spectral energy distributions (SEDs), after subtracting a hotdust, PL component with three possible spectral indices α = 1.3, 2.0, and 3.0. I obtain that 35% of these 24 μm sources are powerlaw composite galaxies (PLCGs), which I define as those galaxies for which the SED fitting with stellar templates, without any previous PL subtraction, can be rejected with >2σ confidence. (Abstract excerpt) Cecchini, Chiara, et al. Testing scaleinvariant inflation against cosmological data. arXiv:2403.04316. University of Trento, Italy and University of Sheffield, UK physicists Into 2024, provide a strongest affirmation of nature’s intrinsic selfsimilarity across the breadth and depth of the celestial raiment. In this present regard, the fractallike property extends to and holds for the universe’s initial expansion. See also Observational tests in scale invariance I and II: galaxy clusters and rotation of galaxies by Andre Maeder arXiv:2403.08759 and 2403.08379. There is a solid theoretical and observational basis behind scaleinvariance as a fundamental symmetry of Nature. We consider a recent classical inflationary model that is quadratic in curvature with a scalar field coupled to gravity. By our approach, the twofield dynamics of the system can be solved based on the latest Cosmic Microwave Background (CMB) data from Planck and BICEP/Keck. Overall, we argue that scaleinvariant inflation possesses features which make it an interesting benchmark for tests of inflation from future CMB data. Chang, Tom, et al. Complexity, Forced and/or SelfOrganized Criticality, and Topological Phase Transitions in Space Plasmas. Space Science Reviews. 107/12, 2003. Astronomers from MIT, UCLA, and the Institute of Physics of Interplanetary Space, Rome, enter a prescient example of the growing realizations of an inherently nonlinear celestial environment, in every aspect. The first definitive observation that provided convincing evidence indicating certain turbulent space plasma processes are in states of ‘complexity’ was the discovery of the apparent powerlaw probability distribution of solar flare intensities. Recent statistical studies of complexity in space plasmas came from the AE index, UVI auroral imagery, and insitu measurements related to the dynamics of the plasma sheet in the Earth's magnetotail and the auroral zone. (425) Chanu, Athokpam, et al. Analysis of the structural complexity of Crab Nebula observed at radio frequency using a multifractal approach. Journal of Physics: Complexity. volume 5, 2024. As Earthuman celestial studies proceed apace, five researchers posted at Asia Pacific Center for Theoretical Physics, Korea, Indian Institute of Astrophysics, Bangalore, Pondicherry University, Jawaharlal Nehru University, and National Centre for Radio Astrophysics, Tata Institute of Fundamental Research, India report another instance of astronomic selfsimilarities as they apparently suffuse a genesis universe. The Crab Nebula is an astrophysical system that exhibits morphological patterns at different observing frequencies. We investigate the structural complexity of the nebula using imaging data at radio frequency. We use the wellknown multifractal detrended fluctuation analysis in two dimensions and find that radio data exhibit longrange correlations from the underlying physics of the supernova explosion and evolution. The correlations follow a powerlaw scaling with length scales. The structural complexity is found to be multifractal in nature, as evidenced by the the generalized Hurst exponent. Our analysis thus provides a fresh perspective on the morphology of the Crab Nebula from a complexity science viewpoint. (Excerpt) Charbonneau, Patrick, et al. Fractal Free Energy Landscapes in Structural Glasses. Nature Communications. 5/3725, 2014. A team of American, French and Italian physical chemists including Giorgio Parisi describe how these selfsimilar topologies distinguish particle density transitions in such amorphous materials. In regard, as the Abstract cites, see also a 2016 paper Scaling Ansatz for the Jamming Transition by Carl Goodrich, et al (PNAS 113/9745) which displays an “emergent scaleinvariance.” Glasses are amorphous solids whose constituent particles are caged by their neighbours and thus cannot flow. This sluggishness is often ascribed to the free energy landscape containing multiple minima (basins) separated by high barriers. Here we show, using theory and numerical simulation, that the landscape is much rougher than is classically assumed. Deep in the glass, it undergoes a ‘roughness transition’ to fractal basins, which brings about isostaticity and marginal stability on approaching jamming. Critical exponents for the basin width, the weak force distribution and the spatial spread of quasicontacts near jamming can be analytically determined. Their value is found to be compatible with numerical observations. This advance incorporates the jamming transition of granular materials into the framework of glass theory. Because temperature and pressure control what features of the landscape are experienced, glass mechanics and transport are expected to reflect the features of the topology we discuss here. (Abstract) Chown, Marcus. All the World’s a Hologram. New Scientist. January 17, 2009. Each week this magazine has a cover story with spectacular claims, always intriguing, often true. In this case spurious results from the GEO600 satellite gravitational wave search seem to affirm Fermilab physicist Craig Hogan quantum theories that predict a breakdown or shift at Planck scale lengths or edges from a continuum into a pixilated state that might imply a fundamental holographic reality. If spacetime is a grainy hologram, then you can think of the universe as a sphere whose outer surface is papered in Planck lengthsized squares, each containing one bit of information. The holographic principle says that the amount of information papering the outside must match the number of bits contained inside the volume of the universe. (26) Chumak, Oleg and Alexey Rastorguev. Kinetic Properties of Fractal Media. arXiv:1604.04449. When we first posted this section in 2004, the selfsimilar nature of celestial reaches was much in question. A dozen worldwide years later this quality is commonly assumed in astrophysical papers. Here a Moscow State University astronomer and a physicist attest to its robust presence in many forms and movements. Kinetic processes in fractal stellar media are analyzed in terms of the approach developed in our earlier paper (1511.03818) involving a generalization of the nearest neighbor and random force distributions to fractal media. Diffusion is investigated in the approximation of scaledependent conditional density based on an analysis of the solutions of the corresponding Langevin equations. It is shown that kinetic parameters (time scales, coefficients of dynamic friction, diffusion, etc.) for fractal stellar media can differ significantly both qualitatively and quantitatively from the corresponding parameters for a quasiuniform random media with limited fluctuations. The most important difference is that in the fractal case kinetic parameters depend on spatial scale length and fractal dimension of the medium studied. A generalized kinetic equation for stellar media (fundamental equation of stellar dynamics) is derived in the FokkerPlanck approximation with the allowance for the fractal properties of the spatial stellar density distribution. (Abstract) Coley, A. A. Dynamical Systems and Cosmology. Dordrecht: Kluwer Academic, 2003. The assumption of an invariant, dynamically evolving selfsimilarity for cosmological models is said to provide a manageable mathematical complexity. CondeSaavedra, G., et al. Fractal Analysis of the Galaxy Distribution in the Redshift Range 0.45 < Z < 5.0. Physica A. Online September, 2014. Universidade Federal do Rio De Janeiro astrophysicists advance a theory of “relativistic fractal cosmology” to affirm some two decades of research upon an evident hierarchical selfsimilarity across the celestial raiment.
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