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[hal-01921690] New predictions from the logotropic model

(22/10/2021)  
In a previous paper (Chavanis, 2015) we have introduced a new cosmological model that we called the logotropic model. This model involves a fundamental constant Λ which is the counterpart of Einstein’s cosmological constant in the Λ CDM model. The logotropic model is able to account, without free parameter, for the constant surface density of the dark matter halos, for their mass–radius relation, and for the Tully-Fisher relation. In this paper, we explore other consequences of this model. By advocating a form of “strong cosmic coincidence” we predict that the present proportion of dark energy in the Universe is Ωde,0=e∕(1+e)≃0.731 which is close to the observed value. We also remark that the surface density of dark matter halos and the surface density of the Universe are of the same order as the surface density of the electron. This makes a curious connection between cosmological and atomic scales. Using these coincidences, we can relate the Hubble constant, the electron mass and the electron charge to the cosmological constant. We also suggest that the famous numbers 137 (fine-structure constant) and 123 (logotropic constant) may actually represent the same thing. This could unify microphysics and cosmophysics. We study the thermodynamics of the logotropic model and find a connection with the Bekenstein-Hawking entropy of black holes if we assume that the logotropic dark fluid is made of particles of mass mΛ∼ħΛ∕c2=2.08×10−33eV∕c2 (cosmons). In that case, the universality of the surface density of the dark matter halos may be related to a form of holographic principle (the fact that their entropy scales like their area). We use similar arguments to explain why the surface density of the electron and the surface density of the Universe are of the same order and justify the empirical Weinberg relation. Finally, we combine the results of our approach with the quantum Jeans instability theory to predict the order of magnitude of the mass of ultralight axions m∼10−23eV∕c2 in the Bose–Einstein condensate dark matter paradigm.

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Smoluchowski-Poisson Dissipation Fermi gas Denaturation Statistical Mechanics Smoluchowski equation Virial theorem Fokker-Planck Cosmological model Generalized thermodynamics Phase separation Entropy Dark matter Physique statistique 9530Sf Brownian motion Bethe ansatz Quasicrystals Effondrement gravitationnel Théorème du viriel Phase transition Dark matter halo Glass transition Violent relaxation Ions close to interfaces Statistical and Nonlinear Physics Collapse Rotation 9880-k Potential quantum TASEP Random tilings Critical phenomena Einstein Axion star Gravitation Turbulence Gravitation collapse Hydrodynamics Temperature Scalar field Polytrope Numerical calculations Chemotaxie 9536+x Poisson equation Scalar field theory Atmosphere Evaporation Axion Random process Metastable states Transition vitreuse Mouvement brownien 9862Gq Dark matter condensation Energy high Cosmology Competition Long-range interactions Bose–Einstein condensates General relativity Perturbation theory Game theory Collisionless stellar-systems Chemotaxis Diffusion Scattering length Computational modelling Thermodynamics Gravitational collapse Quantum mechanics Statistical mechanics Stability Black hole Nonrelativistic Euler-Maclaurin Marcheur aléatoire Suppression Processus stochastique Wave function 9535+d Interacting agents DNA Persistence Wisdom of crowds Self-organization Parametrization Membrane transport Keller-Segel Catastrophe theory Self-gravitating systems Condensation Bose-Einstein Gravitation self-force Formation Random walker Quantum chromodynamics axion Field theory scalar Structure Nanofiltration