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

E. Systems Cosmology: Fractal SpaceTimeMatter

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 self-similar 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, power-counting 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 four-dimensional 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)

Despite their diversity, many of the most prominent candidate theories of quantum gravity share the property to be effectively lower-dimensional at small scales. In particular, dimension two plays a fundamental role in the finiteness of these models of Nature. Thus motivated, we entertain the idea that spacetime is a multifractal with integer dimension 4 at large scales, while it is two-dimensional in the ultraviolet. Consequences for particle physics, gravity and cosmology are discussed. (Abstract, "Gravity on a Multifractal" Physics Letters B (697/251, 2011.

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 axion-like particles. The fractal self-similar structure of the thermal radiation is also discussed and related to the coherent structure of the thermal vacuum. (Abstract)

Caputi, Karina. A Generalized Power-Law 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, Argentine-Dutch researcher finds a power-law scale invariance to take manifest form everywhere. See then in this issue “Cosmic Emulation: The Concentration-Mass 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 power-law (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 rest-frame UV/optical/near-IR spectral energy distributions (SEDs), after subtracting a hot-dust, 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 power-law 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)

Chang, Tom, et al. Complexity, Forced and/or Self-Organized Criticality, and Topological Phase Transitions in Space Plasmas. Space Science Reviews. 107/1-2, 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 power-law probability distribution of solar flare intensities. Recent statistical studies of complexity in space plasmas came from the AE index, UVI auroral imagery, and in-situ measurements related to the dynamics of the plasma sheet in the Earth's magnetotail and the auroral zone. (425)

In this review, we describe a theory of dynamical ‘complexity’ for space plasma systems far from equilibrium. We demonstrate that the sporadic and localized interactions of magnetic coherent structures are the origin of ‘complexity’ in space plasmas. Such interactions generate the anomalous diffusion, transport, acceleration, and evolution of the macroscopic states of the overall dynamical systems. (425)

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 self-similar 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 scale-invariance.”

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 quasi-contacts 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 space-time is a grainy hologram, then you can think of the universe as a sphere whose outer surface is papered in Planck length-sized 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 self-similar 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 scale-dependent 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 quasi-uniform 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 Fokker-Planck 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 self-similarity for cosmological models is said to provide a manageable mathematical complexity.

Conde-Saavedra, 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 self-similarity across the celestial raiment.

Conde-Saavedra, Gabriela, et al. Fractal Analysis of the Galaxy Distribution in the Redshift Range 0.45 < Z < 5.0. arXiv:1409.5409. In the mid 2010s, Universidade Federal do Rio de Janeiro astrophysicists are able to quantify and affirm the presence of self-similar galactic topologies. A fractal cosmos is indeed actually there. Wherever then did all this intrinsic lively structure, which equally graces and informs life and persons, originally come from?

Cosmai, Leonardo, et al. Fractal Universe and Cosmic Acceleration in a Lemaitre-Tolmon-Bondi Scenario. arXiv:1810.06318. When we began this section in the early 2000s, the presence of self-similar structures was suspected but their verification, still open to question, across many scales was just beginning. Here Italian astrophysicists including Luciano Pietronero and Francesco Labini (search each) can now affirm, some 90 years after Lemaitre and 4 centuries after Galileo, that an intrinsic mathematical geometry does indeed suffuse the celestial raiment.

In this paper we attempt to answer the question: can cosmic acceleration of the Universe have a fractal solution? We give an exact solution of a Lemaitre-Tolman-Bondi (LTB) Universe based on the assumption that such a smooth metric is able to describe, on average, a fractal distribution of matter. While the LTB model has a center, we speculate that, when the fractal dimension is not very different from the space dimension, this metric applies to any point of the fractal structure when chosen as center so that there is not any special point or direction. We examine the observed magnitude-redshift relation of type Ia supernovae, showing that the apparent acceleration of the cosmic expansion can be explained as a consequence of the fractal distribution of matter. (Abstract)

Coutinho, Bruno, et al. The Network Behind the Cosmic Web. arXiv:1604.03236. A Boston-based team of system and astro physicists including Albert-Laszlo Barabasi and Mark Vogelsberger provide a strongest statement to date of the presence across galactic reaches of the same scale-free topologies as everywhere else in nature and society. A longer technical version is posted as Discriminating Topology in Galaxy Distributions using Network Analysis at arXiv:1603.02285. And this reference is being logged in along with a paper by Semi Min and Juyong Park on Narrative Structures and Dynamics Using Networks (1604.03029) which notes that even literary classics exhibit these common qualities. In our midst, might a realization dawn of a “deep universality” from cosmos to culture, a truly textual nature?

The concept of the cosmic web, viewing the Universe as a set of discrete galaxies held together by gravity, is deeply engrained in cosmology. Yet, little is known about the most effective construction and the characteristics of the underlying network. Here we explore seven network construction algorithms that use various galaxy properties, from their location, to their size and relative velocity, to assign a network to galaxy distributions provided by both simulations and observations. We find that a model relying only on spatial proximity offers the best correlations between the physical characteristics of the connected galaxies. We show that the properties of the networks generated from simulations and observations are identical, unveiling a deep universality of the cosmic web. (Abstract)

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