Physical Sciences

Abstract: We examine phenomenological consequences of a scale-dependent gravity model in which the gravitational coupling runs with the cosmological scale factor as G(a)=G0an. In the companion paper, this running was shown to modify the Friedmann equation through effective starred couplings and to produce corresponding changes in the Wheeler–DeWitt minisuperspace potential. For values of n, we ask whether the same running can survive into observationally tested epochs. Applying three consistency tests—the expansion rate during Big-Bang nucleosynthesis, the growth of linear matter perturbations, and the CMB acoustic scale—we find that BBN and CMB consistency require n to be very small if the power-law form persists to nucleosynthesis or recombination. These tests constrain the epoch over which the pure power-law form can remain valid. The power-law running is best considered as an early-universe scaling regime that must shut off before nucleosynthesis — the question is not whether, but when and how. Any realistic extension of the strong-running regime must cut off, screen, or smoothly transition the gravitational coupling back to standard gravity before the nucleosynthesis era.

Abstract: We show that a logarithmic gravitational potential emerges from the classical phase-space geometry of the Keplerian 1/r interaction together with a phenomenological weak-field statistical ansatz. The number of accessible phase-space cells in a 1/r potential scales as N(r)∝rη, where η is determined by the effective dimension of accessible action space (η=1 for rotationally constrained disks, η=3/2 for isotropic spherical systems), yielding a logarithmic Boltzmann entropy S(r)∼ηkBlnr for any η. The effective logarithmic potential then follows from the potential of mean force after integrating out internal Keplerian phase-space degrees of freedom, F=ΦN−ΘHσ, where the effective energy scale ΘH is identified with the depth of the Newtonian potential well at the cosmological transition radius, introducing no free parameters. The resulting framework naturally reproduces flat galactic rotation curves, the baryonic Tully–Fisher relation v_c⁴=GM_ba₀ where a₀∼cH₀ is the empirical BTFR acceleration scale, and the weak-field lensing signature of isothermal halos. Three parameter-free comparisons against 357 unique galaxies from the SPARC and ATLAS3D surveys confirm the predicted scalings, including a parameter-free prediction for the velocity dispersion of early-type galaxies (σ/e4=3/8GM_ba₀, R²=0.856, N=231), whose coefficient arises from an η=3/2 isotropic action-space geometry distinct from the η=1 disk relation. The framework is developed as a phenomenological statistical theory and does not claim to replace a complete microscopic description of dark matter at all scales.

Abstract:

It is a famous old problem: Why the orbit of the Moon around the Earth is stable under the condition that, calculated with F=GMm/R², the force of the Sun on the orbit is almost 2.2 times that of the Earth? We find, the calculated force of the Sgr A* on the orbit of the Oort cloud around the Sun is larger than that of the Sun; and, the force of the Sgr A* on the orbits on the edge of the ω Centauri is larger than that of the black hole at the center of the ω Centauri. It is known that the old problem about the Moon around the Earth can be understood with the Newtonian theory of orbit perturbation. Here, we find, the problem about the Oort cloud and the ω Centauri also can be understood with the Newtonian theory of orbit perturbation. And, we conclude that the mass of the Sgr A* should be M_SgrA*∼1.8×10¹¹M_Sun ; and, at the center of every stellar cluster there should be a black hole or other massive body which can be easily measured with any one of the orbits in the cluster or with the Hill sphere.

Abstract:

Galactic rotation curve was formulated before the Sgr A* had been confirmed. The action of the Sgr A* on the rotation curve has not been considered. Now, it was observed that the fastest stars in the Milky Way is in the distance less than 0.5pc from the Sgr A*. It is contradicted with the current galactic rotation curve in which the orbital velocity near the center of the galaxy is the smallest. And, because of the advance of technology, it was observed that the circular velocity curve of the Milky Way from 5 to 30 kpc is with a significantly faster decline (Keplerian decline) compared to the inner parts. It is contradicted with the current curve in which the out parts could be larger or no decline. And, it was observed that the fast galaxy bar continue challenge the standard cosmology. For the reasons, we present an improved galactic rotation curve.

Abstract: The minimalist approach for linear stability analysis is applied to fluids and magnetized ideal plasmas in cylindrical geometry. In this approach, the dispersion relation is obtained by integrating a single first-order differential equation – referred to as the principal equation – subject to appropriate boundary conditions. We first derive the principal equation for a general unperturbed state with radially varying density and pressure, axial and azimuthal components of both the velocity and magnetic field, and a radially directed gravitational field. We then use this formulation to analyze rotating flows with axial magnetic fields, addressing both wall-bounded and interface-driven axisymmetric instabilities. In addition to exact results for selected unperturbed states, we obtain approximate dispersion relations using the WKBJ method in the incompressible and compressible limits. The analysis encompasses centrifugal, magnetorotational, and buoyancy-driven instabilities as special cases, and it clarifies how compressibility modifies their stability properties.

Abstract: Upper-level wind and spatial inhomogeneities in the vorticity field are the key characteristics of atmospheric turbulence. In this paper, we study the spatial and temporal variations in wind speed and atmospheric vorticity within the layer 9.5–13.6 km (300 - 150 hPa) at the site of Special Astrophysical Observatory (SAO). Using hourly data from the ERA-5 reanalysis over a ten-year period, from 2016 to 2025, we obtained seasonal spatial distributions above SAO and evaluated long-term trends using the non-parametric Mann–Kendall test. Analysis of the spatial distributions reveals the subregion with strong upper-level winds southeast of the observatory during winter, spring, and autumn. In summer, the subregion shifts northward due to dynamics of frontal zone and jet stream. Three-dimensional atmospheric vorticity fields exhibit complex, multi-layered, and localized structures. The spatial inhomogeneity of vorticity field acts as an indicator of local optical turbulence. Jet stream winds and the associated wind shears at the 200 hPa pressure level are primary drivers of tropospheric optical turbulence. It is important to emphasize that the optical turbulence strenght depends on the specific location of the jet stream. Turbulence is suppressed within the jet stream while the repeatability of turbulent fluctuations increases significantly at its periphery. Long-period trend assessments indicate a statistically significant decrease in winter wind speeds (-0.0028 to -0.0060 m/s per night, p ≤ 0.01), as well as a significant decrease in winter local vorticity at heights of 12.8–13.6 km (-0.0007 to -0.0011 1/s per night, p ≤ 0.04). These changes are linked to the global (arctic) warming and reduced latitudinal large-scale temperature contrasts. A systematic decrease in wind speed should lead to a decrease in total atmospheric turbulence (the kinetic energy of flow should tend to decrease). However, turbulence can be additionally generated locally due to the deformations of large-scale jet stream. Conversely, summer profiles show a robust and significant increase in wind speed (up to 0.0038 m/s per night, p ≤ 0.04). Long-period changes in vorticity are not significant. For comparison, trends in the optical turbulence strength at the Baikal Astrophysical Observatory are analyzed. Analysis of data obtained make it possible to note that in the summer-autumn period, when the quality of astronomical images is the best, one can expect a deterioration in conditions for astronomical observations under the influence of climate changes.

Abstract: The creative combination of Gabriel horn (G-horn) hyperboloid with Finsler geometry opens a new door to black holes. G-horn with finite volume but infinite surface area can characterize the frame-dragging effects of strong gravitational fields. Finsler geometry is used to describe gravitational bounce depending on velocity direction. On the smooth and inextendible manifold representing by G-horn’s inner surface, the torsion determined by Cartan connection gives rise to centrifugal force and Coriolis force to counteract gravitational collapse. The Coriolis force serves as spin-flip trigger for gravitational bounce. The entering matters are choked at a certain inner-surface zone of horn’s neck as a novel non-Penrose’s trapped surfaces with global geodesic completeness, and forms a regular “hollow” core. Without any hidden or naked singularities, the mathematical singularity and the center of matter accumulating region need not coincide. By developing Cartan torsion-decomposing method, the competition mechanism between gravity of curvature and the “centrifugal force ± Coriolis force” of torsion is a elegant solution to those existing paradoxes or hypotheses such as black hole information loss, Penrose’s cosmic censorship, Weinberg’s asymptotically safe gravity. Further, the Schwarzschild, Kerr, Reissner‑Nordström black holes may be modified uniformly as this “singularity‑free” G-horn model.

Abstract: We study an effective quantum cosmological model with a scale-dependent gravitational coupling G(a). Starting from a quantum-corrected Newtonian cosmology, we derive a modified Friedmann equation and quantize the corresponding minisuperspace model to obtain a Wheeler–DeWitt equation. For the power-law running G(a)=G0an, the small-scale behavior is controlled by the exponent n. In the flat dust model with a positive quantum correction term Ξ, the values n=3/2 and n=2 mark distinct analytic boundaries: n=3/2 marks the sign change of the quantum-correction coefficient, while n=2 marks the degeneracy of the leading powers of a. A genuine bounce occurs only when a root of H2(a) separates a forbidden small-a region from an allowed expanding branch, so that nonsingular sectors appear without spatial curvature, exotic matter, or nonstandard quantization prescriptions. We obtain Bessel, Airy, numerical, and WKB solutions, and show that the model separates genuine DeWitt suppression from regularity at the origin. The WKB analysis exhibits a forbidden region, a turning point, and an oscillatory semiclassical branch, while the conserved probability current distinguishes expanding and contracting sectors. A scalar-field clock yields wave packets that track the classical trajectory at large scale factor; the WKB Hamilton–Jacobi limit recovers the modified Friedmann dynamics as the leading-order phase of the Wheeler–DeWitt wave function.

Abstract: We investigate the variational principle for a finite Friedmann–Lemaître–Robertson–Walker (FLRW) spacetime matched to an exterior vacuum. Requiring a well-defined Einstein–Hilbert action leads to a moving junction whose stationarity enforces continuity of the induced metric and extrinsic curvature across the boundary. The resulting junction conditions admit two physically distinct branches. A comoving branch reproduces the pressureless Oppenheimer–Snyder solution, while a second, non-comoving branch arises whenever pressure is present. We show that this branch is uniquely selected by causality and approaches a universal attractor, independent of spatial curvature and valid for both expanding and collapsing solutions. Within this framework, the effective cosmological constant emerges as a geometric consequence of the causal boundary rather than as an independent bulk parameter. The variational principle remains well defined even when the effective cosmological constants differ across the junction, allowing the interior and exterior spacetimes to possess different vacuum energies while preserving continuity of the geometry. The non-comoving branch provides an exact extension of the Oppenheimer–Snyder interior solution to the physically relevant case of non-zero pressure and predicts a maximum causally connected angular scale, defining a new cosmological probe of the causal boundary. For the observed cosmological constant, the predicted cutoff at recombination agrees with the measured large-angle homogeneity scale of the cosmic microwave background. The infinite FLRW limit is recovered as the boundary radius tends to infinity, for which the effective cosmological constant vanishes. Within this framework, the observed non-zero cosmological constant points to a finite gravitating FLRW region bounded by a causal horizon whose asymptotic radius coincides with its Schwarzschild radius.

Abstract: The old Le Sage’s hypothesis on the corpuscular origin of gravity is revisited and reassessed. The discussion is developed along three lines: the “modern” wave approach, a “mass–flux” of a relativistic fluid model, and the traditional corpuscular model. The predictions obtained in all the three approaches are convergent with other current attempts. The main outcomes are the emergence of a maximal gravitational acceleration – compatible with the surface gravity of neutron stars – and the absence of gravitational field divergences for arbitrarily large or collapsed masses. The resulting theory differs from classical Newtonian gravity in its much clearer separation between the concepts of heavy and inert mass, a distinctive characteristic of the Le Sage-type (or “shadow gravity” or “Push–Gravity” (PG)) theories. The price to pay is a departure from the equivalence principle in its weak form, which might no longer be considered rigorously valid. We will only touch on the issue of experimental verification, which remains very difficult: the simple test we propose here is more a rough estimate of gravity at the Earth’s equator and poles using PG theory, which indicates only qualitative agreement with the gravimetric data. In the end, a cosmological speculation has been added, based on Le Sage’s idea, which is discussed at a preliminary and tentative level.

Abstract: Galaxy rotation curves alone no longer provide a decisive test between dark matter and its main alternatives. Standard halo models, relativistic MOND theories, and the recently proposed κ-Model can all reproduce the observed kinematics of spiral galaxies with comparable accuracy. The central problem is therefore to identify observables capable of breaking this degeneracy. In this work, we compare MOND and the κ-Model for four isolated galaxies by combining rotation-curve constraints with gravitational lensing predictions. In both dark matter and relativistic MOND frameworks, the velocity field and the lensing signal are expected to arise from the same effective gravitational mass distribution. The κ-Model instead offers a different interpretation: galactic dynamics and lensing distortions need not be governed by a single large-scale mechanism, since they reflect distinct aspects of the anamorphic mapping between physical and observational space. We argue that the outer regions of isolated galaxies provide the most favorable regime for testing this distinction. In the κ-framework, the asymptotic lensing behavior predicts a specific relation between the gravitational shear and the projected mass density around the galaxy. The measured shear is therefore not merely a consequence of the dynamical mass reconstruction, but also encodes the geometric structure of the observational bundle. Consequently, a systematic mismatch between the lensing signal inferred from dynamics and that obtained directly from gravitational shear measurements would challenge the common assumption, shared by dark matter and relativistic MOND theories, that a single effective mass distribution simultaneously accounts for galactic kinematics and lensing. Although speculative, this hypothesis is directly testable and hence falsifiable. If such a discrepancy were observationally established, it would provide a clear empirical signature in favor of the κ-framework and would rule out, in its standard form, the paradigm according to which the same underlying mass component is responsible for both galaxy rotation curves and gravitational lensing.

Abstract: The cislunar space, governed by the circular restricted three-body problem (CR3BP), presents significant challenges for mission design due to its complex stability structure. Traditional high-fidelity numerical integration is computationally prohibitive for a systematic energy-regime census of millions of orbits. Here, we present a novel approach based on global volunteer computing via the BOINC platform to overcome this barrier. Using the public “Million Orbit” dataset from Lawrence Livermore National Laboratory, we distributed the computation of Jacobi constant time series across thousands of volunteer devices, producing over 16 billion individual values. The resulting dataset is freely available. Analysis reveals that 91.68% of orbits belong to the high-energy Region V, 8.07% to the low-energy Region I, and only 0.24% to Region III, with Region II completely absent. A single rare Region IV orbit (ID 754482) was identified and analyzed. Furthermore, we develop a lightweight deep learning surrogate that predicts whether an orbit belongs to the low-energy Region I using only the first K Jacobi constants (prefix). Our model combines an LSTM encoder with attention and an XGBoost classifier, achieving test AUC of 0.984 with K = 500 and 0.929 even with K = 10, outperforming a raw XGBoost baseline. This work demonstrates the transformative potential of volunteer computing for large-scale astrodynamics and provides an efficient machine learning tool for real-time orbit screening. Our attention analysis further reveals that the model automatically focuses on the initial transient for long sequences, quantitatively confirming the sensitive dependence on initial conditions in the Earth-Moon system.

Abstract: General relativity and quantum mechanics have nominally incompatible perspectives on the nature of spacetime, which has been problematic for a “theory of everything” that would unite gravity with the other three forces. We introduce the concept of spacetime duality – that the fabric of spacetime is a separate entity from the material world (matter and energy) that exists upon that fabric. Objects in the material world as well as the spacetime coordinate system of the material world obey quantum mechanics and have wave particle duality. The fabric of spacetime is not a quantum entity. Points in the material coordinate system have both a particle and wave nature by virtue of having both a labeled spacetime position and a wave function for that position that extends over the fabric of spacetime. Physical and mathematical considerations from quantum mechanics and cosmology lead to spacetime duality. The concept is shown to explain some infinities in quantum calculations; provide insight into collapse of the wave function; provide a mechanism for compactification in string theory; leads to a framework for coupling gravity with quantum field theory that provides a simple physical explanation for why gravity is weak relative to the other three forces; resolves the black hole information paradox; and avoids singularities in black holes.

Abstract: This article presents the authors’ proposed theory on the formation of cavitation voids in the false vacuum during the inflationary phase of the Big Bang. It examines the structure of, and the physical processes occurring in, the transition region at the boundary between the false and physical vacuums. It has been demonstrated that, during the formation of physical vacuum voids (regions in which the Λ-term, a constant in the equations of general relativity, goes to zero), conditions arise in the transition region between the false vacuum and the physical vacuum that allow for the formation of a narrow layer of matter. This layer may be the precursor to the bridges observed in the large-scale lattice structure of the universe. The mechanism of bubble expansion during the inflationary phase of the universe is examined. It has been demonstrated that the inflationary phase of expansion passes into the standard Big Bang model due to the conversion of the false vacuum into matter at the boundaries of the bubbles. This model does not require the universe to undergo an extremely rapid expansion to explain the quasi-homogeneous and isotropic distribution of matter and the cosmic microwave background. Furthermore, it can account for the formation of the large-scale lattice structure of the universe. The estimated radii of cosmic voids are consistent with observational data.

Abstract: This paper derives the black-body-equivalent cosmic microwave background (CMB) Hubble-sphere flux implied by the temperature relation $T_{\rm cmb}=\frac{\hbar c}{k_B4\pi\sqrt{2R_Hl_p}}$ inside an assumed $R_H=ct$ cosmological framework. Inserting this temperature directly into the Stefan--Boltzmann radiant-exitance law gives the central result \begin{equation} F_{\rm cmb}=\sigma T_{\rm cmb}^4 =\frac{\hbar c^2}{61440\pi^2R_H^2l_p^2}. \end{equation} Equivalently, when the CMB temperature is written as the geometric mean $T_{\rm cmb}=\sqrt{T_{\max}T_{\min}}$, with $T_{\max}=\hbar c/(k_B8\pi l_p)$ and $T_{\min}=\hbar c/(k_B4\pi R_H)$, the same flux becomes \begin{equation} F_{\rm cmb}=\sigma T_{\max}^2T_{\min}^2. \end{equation} Thus the new result emphasized here is a CMB black-body-equivalent one-sided flux that scales as $F_{\rm cmb}\propto R_H^{-2}$, or equivalently as $t^{-2}$ when $R_H=ct$.

Abstract: The reconstruction of galaxy assembly histories from contemporary stellar populations remains a central challenge in astrophysics. Both stellar population synthesis and Galactic Archaeology represent special cases of the same Bayesian inverse problem: inferring evolutionary history from present-day observables. This unification constitutes the central contribution of the present work. We formalise it as Unified Galactic Reconstruction (UGR), in which the full posterior over the evolutionary state is conditioned simultaneously on chemical and dynamical observables, rather than treating them sequentially. The Starlight Synthesis Algorithm operates as the integrated-light limiting case of UGR, while large-scale chemo-kinematic tomography represents the resolved-star limit. We additionally introduce the Galactic Reconstruction Number, R_G = N_chem × N_kin / N_pop, as a dimensionless heuristic index for comparing reconstruction methodologies. UGR naturally subsumes existing approaches as limiting cases and provides a conceptual foundation for next-generation Galactic studies with forthcoming surveys, including 4MOST, WEAVE, and the Roman Space Telescope.

Abstract: Star formation in Galactic dense clumps is commonly interpreted using nearly uniform protostellar evolutionary timescales, yet the extent to which such assumptions obscure variations in star formation efficiency remains uncertain. Using 60 ATLASGAL dense clumps associated with MIPSGAL Class I protostars and \( \mathrm{NH_3} \) velocity information, we show that compactness and dense-gas evolutionary state provide a stronger explanation of instantaneous and cumulative star formation behavior than adopting a universal Class I lifetime. By combining cumulative efficiencies with a dense-gas star formation calibration, we find that star formation proceeds with systematically mass- and density-dependent timescales, implying that a single evolutionary clock can significantly bias inferred efficiencies across the clump population. The lower-limit cumulative star formation efficiency was observed to increase with decreasing clump radius following \( R_{\mathrm{cl}}^{-1.30 \pm 0.09} \), while no significant correlation is found with Galactocentric radius. Upper- and lower-limit cumulative efficiencies exhibit a sublinear relation with slope \( 0.66 \pm 0.08 \), suggesting possible stellar initial mass function incompleteness. The dense-gas star formation timescale follows \( \tau_{\mathrm{SF,dense}} \propto M_{\mathrm{cl}}^{-0.77 \pm 0.04} \), with a median value of \( 0.54\,\mathrm{Myr} \). Assuming a relatively uniform timescale of \( 0.50\,\mathrm{Myr} \) could overestimate and underestimate star formation rates in low-mass and massive clumps by factors of \( \sim 32 \) and \( \sim 25 \), respectively.

Abstract: We review arguments showing that Big Bang, subsequent cosmic inflation, present accelerating expansion of the universe (dark energy) and lightness of elementary particles have the same physical origin. Namely, these phenomena are manifestations of the negative value of the gravitational field energy in the vector theory of gravity, which causes these effects and yields value of the cosmological constant and masses of elementary particles in excellent agreement with experiment without free parameters. We also explain how arrow of time emerges in vector gravity. According to the latter, universe is a region of 4-dimensional space with geometry of Minkowski signature, embedded in a fixed Euclidean background. The theory predicts that cosmic inflation exponentially expands the spatial size of the universe and exponentially contracts its temporal size. As a result, size of the universe along the temporal dimension is close to zero, and universe as a whole is moving through the Euclidean background along the time direction, which yields a unidirectional flow of time.

Abstract: We believe that the origin of the universal dark energy may crucially depend on the behavior of the gravitational constant G. If G is constant throughout the universe, then the dark energy density u₀ is supported by the vacuum via its constant and evolving properties. On the other hand, in varying-G gravity (whose low-acceleration limit is MOND), u₀ is a manifestation of radial G-gradients in the source of gravity. We estimate the present-day dark energy density of the universe in these two independent cases without using conventional Planck-2018 modeling. The constant-G derivation uses dimensional analysis, vacuum constants, and a newly discovered evolving bridge between vacuum mechanical and electromagnetic quantities. The varying-G derivation relies on the MOND critical acceleration a₀, the source of gravity that falls off as ∼1/r² at large distances r, and the assumption that the Planck-2018 value reflects a volume average over the history of the post-Stoneyan universe, which is nevertheless heavily weighted toward the very recent (observed) past. The agreement between these two determinations and the Planck-2018 results from ΛCDM modeling is outstanding, so much so that the results cannot distinguish clearly between constant-G or varying-G gravity. The analysis further indicates that the Newtonian constant G₀, the MOND constant a₀, and the Planck units of force, power, voltage, and current are vacuum invariants of the same stature as the well-known resistive properties of the vacuum; whereas charge, capacitance, inductance, and various fields are scale-dependent properties evolving in the expanding universe since the Stoney era. Ultimately, the vacuum behaves as a remarkably stiff elastic medium under stress, irrespective of the presence or absence of matter. This property has long been encoded, albeit inconspicuously, in the much discussed Tully-Fisher and Faber-Jackson relations, as well as in the Casimir effect and the field equations of General Relativity.

Abstract: Cosmological tensions, most prominently the H0 and S8 discrepancies, are now understood as global consistency conditions on the underlying cosmological model rather than as isolated anomalies. We formalise this insight as a cosmological consistency triangle with three vertices that any viable cosmological model must populate simultaneously. The first two vertices, background expansion (H0) and present-day growth amplitude (S8), are universal across deviation classes. The third vertex is theory-specific: we give a formal definition that fixes it, up to reparametrisation, by the irreducible function F(z) introduced by the deviation, and demonstrate via counter-examples that the conditions have non-trivial content. We apply the framework to two contrasting deviations from ΛCDM. For f(Q) gravity, the third vertex is the growth shape, summarised by the growth index γ, against which the recent literature is surveyed. For interacting dark energy, it is the perturbation-level coupling diagnostic: we develop an original linear-perturbation analysis of the compartmentalisation model and present numerical predictions for fσ8(z) showing that the linear and non-linear coupling families are degenerate in redshift-shape at matched dimensionless coupling strength, with third-vertex discrimination acting amplitudinally in the strict quasi-static limit. From the third-vertex requirement we derive a five-point diagnostic checklist for IDE-class analyses, with brief applications to early and dynamical dark energy. The framework clarifies why background-only fits constrain at most two vertices of the triangle; DESI DR3, Euclid, the Simons Observatory, CMB-S4 and Einstein-Telescope-class sirens will decisively test whether any current proposal satisfies all three vertices simultaneously.