Abstract: A new non-minimal version of the Einstein-Dirac-axion theory is established. This version of the non-minimal theory describing the interaction of gravitational, spinor and axion fields is of the second order in derivatives in the context of the Effective Field Theory, and is of the first order in the spinor particle number density. The model Lagrangian contains four parameters of the non-minimal coupling and includes, in addition to the Riemann, Ricci tensor and Ricci scalar, the left-dual and right-dual curvature tensors. The pseudoscalar field appears in the Lagrangian in terms of trigonometric functions providing the discrete symmetry associated with axions is supported. The coupled system of extended master equations for the gravitational, spinor and axion fields is derived; the structure of new non-minimal sources appeared in these master equations is discussed. Application of the established theory to the isotropic homogeneous cosmological model is considered; new exact solutions are presented for a few model sets of guiding non-minimal parameters. A special solution is presented, which describes an exponential growth of the spinor number density; this solution shows that spinor particles (massive fermions and massless neutrinos) can be born in early Universe due to the non-minimal interaction with the space-time curvature.

Abstract: A novel approach to cosmic inflation within the framework of a non-commutative Riemannian foliated quantum gravity, built upon a reverse Faddeev–Jackiw symplectic spacetime deformation of the conventional Poisson algebra, is investigated. Friedmann-type dynamical equations, analitycally continued to a complex non-commutative framework, incorporate a modified energy-momentum Riemann tensor and a non-commutative matter-energy potential, highlighting the emergence of quantum gravity topological fluctuation effects on the expansion dynamics of the universe. In this realm, the coupling of UV and IR scales play a central role, providing a natural topological mechanism for inflation and recursal evidences for the generation of relic gravitational waves. These predictions align with a self-consistent description of the transition between the primordial mirror-universe deceleration and present-universe acceleration phases as predict by the Riemann foliated quantum gravity, offering potential connections to observational cosmology.

Abstract: We present a study of relic gravitational waves based on a foliated gauge field theory defined over a spacetime endowed with a noncommutative algebraic-geometric structure. As an ontological extension of general relativity concerning manifolds, metrics and fiber bundles, the space and time coordinates, which conventionally correspond to classical numbers, are replaced in this formulation by complementary quantum dual fields. In this framework, consistently complying within the Bekenstein criterion, combined with the Hawking-Hertog multiverse conception, singularities merge, portrayed into a new cosmic helix-like scale factor, analytically continued to the complex plane. This scale-factor captures the essence of an intricate topological quantum-leap transition between two phases of the branching universe: a contraction phase preceding the surpassed conventional concept of a primordial singularity and a subsequent expansion phase whose transition region between the two phases is characterized by a Riemannian topological foliated structure. The present linearized formulation, underlying a slightly gravitational field perturbation reveals, during the universe phase transition, high sensitivity of the relic gravitational waves amplitudes to the primordial matter and energy content. The present formulation reveals a stochastic homogeneous distributions of gravitational-wave intensities arising from the capture of short and long spacetime scales within the noncommutative algebraic framework. These results are consistent with the expected anticipated future observations of relic gravitational waves, which are expected to fill the universe as a stochastic homogeneous background.

Abstract:

We presented a modified form of Emergent Gravity (EG), using the Holographic Principle and Vopson's Mass-Energy-Information Equivalence Principle (MEIEP). We use MEIEP to distinguish the type of information contained between a black hole and an ordinary gravitating object. We have shown that there is a way to have a model of EG that allows for the First Law of Thermodynamics to be violated at the Planck and Quantum level with a consequence that can be negligible in stellar scale and "corrective" in galactic scale, at the Macroscopic level. Combining the correction imposed by Special Relativity, the model gave results similar to General Relativity without necessarily going geometric in interpretation. Lastly, we have found a way to resolve the problem of quantum decoherence, where quantum entanglement can be unified with gravity.

Abstract: We present a credible and correct validation of the Modified Einstein Spherical (MES) Universe Model, demonstrating its viability as a fundamental framework for modern cosmology and Physics of the Cosmos, challenging ΛCDM. Through advanced numerical simulations and multi-platform cross-validation, we identified Einstein's 1917 closed spherical universe, augmented with three novel geometric corrections: Zaitian Quantum Power Z_jk, Nonlinear Symmetry N_jk, and Chaotic Power C_jk , providing a deep and groundbreaking scientific understanding of the universe evolution. These first-principles corrections, derived from scalar-field extensions to the Einstein-Hilbert action, unify Quantum Entanglement phenomena, Matter-Antimatter Asymmetry, and Spacetime Fluctuations within a single geometric paradigm, replacing the Dark Energy hypothesis with curvature-driven dynamics. The MES framework bridges classical general relativity and quantum cosmology, resolves persistent cosmological tensions, and provides testable predictions. MES achieves remarkable consistency with the observational datasets Planck 2018 CMB, SDSS-IV BAO, and Pantheon+ SN Ia, yielding H₀=68.0±0.8 km/s/Mpc ( χ²=1200, dof = 2499) and reducing Hubble tension below 2σ. MES key features: 1. Dynamic energy density components (ρ_Z∝αa^-4, ρ_N∝βa^-3, ρ_C∝γa^-1 sin⁡(t⁄τ)) that maintain cosmic stability without fine-tuning. 2. A closed geometry that predicts distinct observational signatures, such as CMB polarization (r_corr>0.8 at l<30 ) and low-frequency gravitational waves ( f ~ 10^-3 Hz ).

Abstract: A covariant classical theory of gravity is given assuming absolute flat spacetime and the strong equivalence principle (SEP). It is shown that adherence to these postulates requires that the gravitational field “dimensionally perturbs”—induces fractional length and duration changes—all physical objects at a location universally. Such perturbations are referred to as “gravity shifts,” and it is found that all gravitational phenomena may be determined by them. Two classes of observers emerge in “gravity shift theory”—“natural observers” using gravity shifted instruments as is, applicable for all presently available observations, and “absolute observers” that correct for the gravity shifting applied to instruments. Absolute observers accurately measure quantities, including the absolute spacetime metric as it actually is. Natural observers do not accurately measure quantities, but their system of measurement is observationally consistent, yielding a curved “natural metric” to characterize spacetime. When a local gravitational system is surrounded by a “background system” with negligible curvature effects, its gravity shifting induces a diffeomorphism applied to the local system, yielding satisfaction of the SEP for natural observers. Gravity shift theory is the only existing theory other than general relativity that fully satisfies the SEP, which is required for successful predictions of observations. Using the naturally observed inertial form of physical law in free-fall frames, covariant formulation in all coordinates establishes the natural metric as the universally coupled gravitational metric in physical law. The unique field equation determining gravity shifts, and therefore the natural metric, is developed. The resultant bimetric theory is parameterless, complete, and self-consistent. The field equation yields the observed post-Newtonian natural metric and linearizes to the predictive linearized Einstein equation, which, along with SEP satisfaction, results in successful prediction of a wide variety of observed gravitational phenomena. A supplement is provided that extends the range of prediction verification to include low post-Newtonian order radiation cases, and also the strong-field cases consisting of the properties of black and neutron stars plus nearby matter and light.

Abstract: The expansion of the universe yields two consistent differing values of a Hubble constant depending on the methods of measurement. The aim of this work was to explain the Hubble tension by properties of space corresponding to a radially inhomogeneous metrics. A cosmological model described by this perturbed FLRW metric has zero pressure and exponentially expanding space. But the observed space appears to be compressed in the radial direction. We consider the dependence of the change rate of photon energy on the direction of its motion. It is found applying the principle of the photon's energy integral extremum and the relationship between it and the energy of a material particle obtained using Lagrange mechanics. The change rate of a photon's energy varies depending on whether it moves in a radial direction or has an angular component. The metric coefficients are determined by the difference in measurements of the Hubble constant using gravitational lensing and a distance ladder.

Abstract: Scalar-tensor theories have shown promise in many sectors of cosmology. However, recent constraints from the speed of gravitational waves have put severe limits on the breadth of models such classes of theories can realize. In this work, we explore the possibility of a string-like Horndeski Lagrangian that is equipped with two dilaton fields. This is an interesting low-energy effective string theory that has a healthy general relativity limit. The evolution of a two-dilation coupled cosmology is not well-known in the literature. We explore the tensor perturbations in order to assess the behavior of the model again the speed of gravitational wave constraint. Our main result is that this model exhibits of a class of cosmological theories that is consistent with this observational constraint.

Abstract: We provide quantitative explanations for known ratios of dark-matter effects to ordinary-matter effects, and we suggest qualitative explanations for the rate of expansion of the universe and for lumpiness tensions. Our work features a well-defined specification for dark matter. Our work features a new multipole-expansion method that combines Newtonian gravity and special-relativistic interpretations of properties of objects. Our work adds one integer-centric equation to successful popular modeling. Some solutions of the equation help to quantitatively explain dark-matter-to-ordinary-matter ratios and help to suggest insight regarding galaxy formation, eras in the rate of expansion, the Hubble tension, and the S8 tension.

Abstract: The X-ray timing properties serve as crucial tool to understand the physical mechanism, such as accretion and jet physics, of black hole X-ray binary (BH XRBs). The study carried out a systematic timing analysis of the Swift J1727.8-1613. The observational data come from the Hard X-ray Modulation Telescope (Insight-HXMT) in 2023, when Swift J1727.8-1613 was transitioning from low-hard state (LHS) to the hard-intermediate state (HIMS). We analyzed their power density spectrum （PDS） and find an obvious type-C quasi-periodic oscillations (QPOs) with the QPO frequency increasing from 0.2 Hz to 1.8 Hz. Detailed light curve and power spectral analysis revealed that the root-mean-square (RMS) amplitude of the QPOs gradually decreased from ∼14% to ∼10%. These observational characteristics show excellent agreement with predictions from the Lense-Thirring precession model under the truncated disk scenario, suggesting that the increasing precession frequency results from the inward migration of the inner accretion disk radius.

Abstract: The Hubble tension reveals a growing discrepancy between early- and late-universe measurements of the Hubble constant. We present Mass Damping Theory (MDT) as a classical alternative to dark energy, where mass suppresses spacetime's vibrational freedom, modulating gravity based on cosmic density. As the universe expands and mass disperses, damping weakens and expansion accelerates—mimicking a cosmological constant without invoking vacuum energy. Applying MDT to DESI DR1 galaxy distributions, we reconstruct H(z) and obtain a best-fit H0=72.98±1.5 km/s/Mpc, consistent with local observations and early-universe constraints. MDT offers a unified, geometric resolution to the Hubble tension, predicting late-time acceleration as an emergent feature of evolving spacetime dynamics.

Abstract: The non-baryonic and non-luminous matter - which interacts with gravity alone - that is all pervasive in the Universe is referred to as “Dark Matter (DM)”. In this work, we study the properties of WIMPs (Weakly Interacting Massive Particles), the most favourable candidates for dark matter. We constrain the mass and cross-section of WIMPs by using the data obtained from the different generations of XENON detectors. With the help of the flux of WIMPs passing through the target nuclei using the direct detection method, we analysed the properties of WIMPs. We compared them with different density profiles of DM, such as NFW, Burket, Isothermal, and Einasto. From these analyses, the results indicate that the mass of WIMPs below 40 GeV/c2 is not possible for detection as they are not tightly constrained for this detector.

Abstract: The Solar System is analysed in the framework of the Complete Relativity theory (by the same author). While the main focus is on the Solar System, hypotheses are presented (and tested) on the origin and evolution of planetary systems in general, but also on the evolution of galaxies and the whole observable universe. The analysis confirms the postulates and hypotheses of the main theory and the hypotheses presented here with a significant degree of confidence. Some of these are: relativity in the invariance of physical laws (i.e., existence of discrete vertical energy levels, where each discrete scale of energy effectively represents a universe, associated with the universal running of couplings) and complete relativity in everything, Solar System is a large scale (inflated, in some interpretations) quantum system (Carbon/Beryllium isotope equivalent) with a nucleus in a partially condensed state and components localized in various horizontally and vertically excited states, life is everywhere (e.g., Earth is a particle, but also a living being), although the presence of extroverted complex forms on the surfaces of celestial bodies is generally very limited in time, anthropogenic climate change is only a part of a major mass extinction event (although humanity definitely has a role, the sense of control is an illusion), major extinction events on a surface of a planet are relative extinctions, may be a regular part of transformation and migration of life (not necessarily complex living individuals) below the surface in the process of a planetary equivalent of embryonic neurogenesis.

Abstract: In this paper we propose new entropy of the apparent horizon $S_h=(1/\beta)\arctan(\beta S_{BH})$, where $S_{BH}$ is the Bekenstein--Hawking entropy. As parameter $\beta\rightarrow 0$ one comes to the Bekenstein--Hawking entropy. This allows us to consider the generalised Friedmann--Lema\^{i}tre--Robertson--Walker (FLRW) equations for the barotropic matter fluid with $p=w\rho$ for arbitrary equation of state parameter $w$. We obtain the matter pressure $p$ and density energy $\rho$ corresponding to the apparent horizon. The modified Friedmann's equations are found. The addition term in the second modified Friedmann's equation plays the role of a dynamical cosmological constant. The dark energy density, pressure and the deceleration parameter are found. It was shown that at some parameters $w$ and $\beta$ we can have two phases, acceleration and deceleration or the eternal inflation. The model under consideration by using the holographic principle describes the universe inflation. Thus, we consider the holographic dark energy model with the generalised entropy of the apparent horizon. We shown that entropic cosmology with our entropy proposed is equivalent to cosmology based on the teleparallel gravity with the function $F(T)$. New cosmology based on the generalized entropy can be of interest for a description of inflation and late time of the universe evolution.

Abstract: This research investigates the advanced scientific concepts of space-time curvature, wormholes, and time dilation as fundamental natural principles described in the Quran centuries before their modern discovery. Surah Al-Kahf is particularly significant in this context, as it directly addresses wormholes, space-time curvature, and gravitational effects. To fully comprehend this, firstly we must understand what “Al-Kahf” truly represents in the Quran. This study explores the scientific properties of Al-Kahf and its relation to relativity, gravitational lensing, and space-time warping, etc.While modern science views Spacetime Curvature, wormholes and time dilation etc., as extraordinary phenomena, The Quran presents them as fundamental aspects of the universe, and are also utilized in divine operations—just as it describes the water cycle, planetary motion, and celestial mechanics etc. These principles are not isolated mentions but are woven throughout the Quran, highlighting the Quran’s deep engagement with the fabric of space-time.Among the key Quranic verses that encapsulate this concept, Surah Al-Kahf 18:17 [7] stands as the most crucial, as it directly defines and completes the key properties of Al-Kahf by describing the Spacetime Curvature, bending of light and gravitational lensing effects etc., in a most fascinating and unbelievable way, without any illogical interpretation but direct meaning of verses, from existing translations like Sahih International etc. and we have just converted it into a visual diagram/figure. While an understanding of Al-Kahf as a space-time phenomenon is possible from other Quranic descriptions, verse 18:17 serves as the “ULTIMATE KEY” to establish this concept with certainty. If one fully comprehends Quran 18:17, with Quran 18:25,29 etc. then the true nature of Al-Kahf becomes undeniably clear—revealing its nature of space-time curvature, time dilation, and gravitational lensing etc. This verse is 18:17 not only foundational but also the pinnacle of understanding, ensuring that any doubts regarding Al-Kahf’s relation to relativity and space-time distortions are completely resolved.Furthermore, once one will understand what “Al Kahf” truly represents, it will unlock a deeper understanding of entire (CHAPTER) “Surah Al-Kahf” which can ultimately help us to understand & reveal the secrets of the universe deeply including wormholes, space-time curvature, and gravitational effects, as Al-Kahf is treasure of these things. It is a complete dedicated chapter about wormholes, space-time curvature, and gravitational effects etc. Without grasping the concept of Al-Kahf from the initial part of the chapter, the rest of Surah Al-Kahf cannot be fully comprehended. This foundational understanding is not just limited to this chapter—it extends to the entire Quran, where relativity, time dilation, gravitational lensing, and space-time curvature/Anomalies are referenced in various verses. When we will establish Al-Kahf as a space-time concept, it will illuminate the meaning of other parts of Surah Al-Kahf and numerous other Quranic verses that describes these cosmic principles throughout the Quranic text.By integrating Quranic insights with General Relativity and modern astrophysics, this paper challenges conventional narratives of scientific history, advocating for a reassessment of the Quran’s contributions to humanity’s understanding of space-time and relativity. This interdisciplinary approach highlights that the Quran contains detailed direct descriptions of these cosmic phenomenon (wormholes, space-time curvature, space-time distortions and gravitational effects etc.) that align with cutting-edge physics, reinforcing the need for a historical reevaluation of scientific knowledge.

Abstract: Has Newtonian dynamics been marginalized by modern astronomy since it failed to explain the classical tests of Einstein’s general theory of relativity? To answer this question, this study aims at Newton’s instantaneous interaction and replaced it with the speed of light. We found that this will occur with additional terms to Newtonian dynamics equations in the form of higher-order corrections (v2/c2). When we ignore the propagation speed of gravity, the add-ons disappear and new equations revert to the classical ones. The higher-order corrections now can explain those celestial phenomena which Newtonian dynamics could not explain in the past including the perihelion precession of Mercury, the deflection of light, and the radar echo delay. The calculated results are consistent with the observation data. Furthermore, we found that the orbital velocity of a single star has a slight increase compared to the Kepler orbital velocity. It is assumed that this increase in rotation speed can be superposed by the number of stars under certain conditions, which is explained in this article. The results of the calculated Milky Way’s rotation velocity from this study are consistent with the available observation data. A new possible explanation for dark matter and energy has been proposed.

Abstract: Dark energy is hypothesized to explain both the curvature of the universe and its accelerated expansion, yet its true nature remains elusive. In this paper, we propose a novel approach to explain dark energy using the properties of black holes. By considering the contribution of the energy-momentum tensor of black holes, often neglected in cosmological models, we demonstrate that ignoring this component can lead to the observed effects attributed to dark energy. Furthermore, we explore a logical paradox involving observability and causality, arguing that this paradox supports the isotropic and instantaneous nature of dark energy effects. Finally, we connect our theoretical framework to observational data, particularly the growth of supermassive black holes (SMBHs) and their relationship to cosmic expansion, providing an empirical foundation for our hypothesis.

Abstract: We explore the post-Newtonian formalism in cosmology, using a system of constituent equations that includes a modified first Friedmann equation—incorporating its homogeneous counterpart—alongside the classical Poisson equation. Furthermore, we include the dynamical equations arising from stress-energy tensor conservation. Within this framework, we examine stellar equilibrium under spherical symmetry. By specifying the equation of state, we derive the corresponding equilibrium configurations. Finally, we investigate gravitational collapse in this context.

Abstract: In the present work we suggest a new approach for studying the equilibrium states of an hydrodynamic isothermal turbulent self-gravitating system, as statistical model for a molecular cloud. The main hypothesis is that the local turbulent motion of fluid elements is purely chaotic and can be regarded as a perfect gas. Then the turbulent kinetic energy, per one fluid element, can be substituted for the temperature of chaotic motion of the fluid elements. Using this we write down effective formulae for internal and total energy and the first principal of thermodynamics. Then we obtain expressions for entropy, free energy, and Gibbs potential. Searching for equilibrium states we explore two possible systems: the canonical ensemble and the grand canonical ensemble. Studying the former we conclude that there is no extremum for the free energy. In the latter system we obtain a minimum for the Gibbs potential when macro-temperature and pressure of the cloud are equal to those of the surrounding medium. This minimum corresponds to a possible stable local equilibrium state of our system.

Abstract: A century ago, Einstein revolutionized physics with his theory of relativity, showing that space and time are not the same for everyone. They can be altered depending on gravity and speed an object experiences. Previous studies argued that human space and time perception also work according to Einstein's general relativity theory by proving that in weightlessness astronauts tended to underestimate distances and time durations due to the absence of the gravitational reference. The current research was intended to further support this argument by assessing whether the subtle changes in gravity, such as made by the moon’s orbital period, can alter human time perception on Earth during everyday activities. The results of the experiments showed that relative to the time when the moon is in medium distance from Earth, there is underestimation of perceived time duration, when the moon’s position is close to perigee.