Search Results (468)

The cosmological constant (CC, $\Lambda$) problem stands as one of the most profound puzzles in the theory of gravity, representing a remarkable discrepancy of about 120 orders of magnitude between the observed value of dark energy and its natural expectation from quantum field theory. This paper synthesizes two innovative paradigms—holographic naturalness (HN) and pre-geometric gravity (PGG)—to propose a unified and natural resolution to the problem. The HN framework posits that the stability of the CC is not a matter of radiative corrections but rather of quantum information and entropy. The large entropy $S_{\mathrm{dS}}\sim M_{\mathrm{P}}^2/\Lambda$ of the de Sitter (dS) vacuum (with $M_{\mathrm{P}}$ being the Planck mass) acts as an entropic barrier, exponentially suppressing any quantum transitions that would otherwise destabilize the vacuum. This explains why the universe remains in a state with high entropy and relatively low CC. We then embed this principle within a pre-geometric theory of gravity, where the spacetime geometry and the Einstein–Hilbert action are not fundamental, but emerge dynamically from the spontaneous symmetry breaking of a larger gauge group, SO($1,4$)→SO($1,3$), driven by a Higgs-like field ${\varphi }^A$. In this mechanism, both $M_{\mathrm{P}}$ and $\Lambda$ are generated from more fundamental parameters. Crucially, we establish a direct correspondence between the vacuum expectation value (VEV) v of the pre-geometric Higgs field and the de Sitter entropy: $S_{\mathrm{dS}}\sim v$ (or $v^3$). Thus, the field responsible for generating spacetime itself also encodes its information content. The smallness of $\Lambda$ is therefore a direct consequence of the largeness of the entropy $S_{\mathrm{dS}}$, which is itself a manifestation of a large Higgs VEV v. The CC is stable for the same reason a large-entropy state is stable: the decay of such state is exponentially suppressed. Our study shows that new semi-classical quantum gravity effects dynamically generate particles we call “hairons”, whose mass is tied to the CC. These particles interact with Standard Model matter and can form a cold condensate. The instability of the dS space, driven by the time evolution of a quantum condensate, points at a dynamical origin for dark energy. This paper provides a comprehensive framework where the emergence of geometry, the hierarchy of scales and the quantum-information structure of spacetime are inextricably linked, thereby providing a novel and compelling path toward solving the CC problem. Full article

In this work, we analyze the dynamical evolution of locally rotationally symmetric anisotropic cosmological models of Bianchi type I (flat curvature) and Bianchi type III (open curvature) within a noncommutative phase space framework characterized by a deformation parameter $\gamma$. Using a Hamiltonian formulation based on Schutz’s formalism for a perfect radiation fluid, we introduce noncommutative Poisson brackets that allow for geometric corrections to commutative dynamics. The resulting equations are solved numerically, which allows for the study of the impact of $\gamma$ and the energy density C on the expansion of the universe and the evolution of anisotropy. The results show that $\gamma <0$ improves expansion and favors isotropization, while $\gamma >0$ tends to slow expansion and preserve residual anisotropy, especially in the open curvature model. It is estimated that the influence of noncommutativity was significant during the early stages of the universe, decreasing toward the present time, suggesting that this approach could serve as an effective alternative to the cosmological constant in describing the evolution of the early universe. Full article

The persistent Hubble tension—marked by a notable disparity between early- and late-universe determinations of the Hubble constant $H_0$—poses a serious challenge to the standard cosmological framework. Closely linked to this is the $H_0-r_d$ tension, which stems from the fact that BAO-based estimates of $H_0$ are intrinsically dependent on the assumed value of the sound horizon at the drag epoch, $r_d$. In this study, we construct a scalar field dark energy model within the framework of a spatially flat Friedmann–Lemaitre–Robertson–Walker model to explore the dynamics of cosmic acceleration. To solve the field equations, we introduce a generalized extension of the standard Lambda Cold Dark Matter model that allows for deviations in the expansion history. Employing advanced Markov Chain Monte Carlo techniques, we constrain the model parameters using a comprehensive combination of observational data, including Baryon Acoustic Oscillations, Cosmic Chronometers, and Standard Candle datasets from Pantheon, Quasars, and Gamma-Ray Bursts (GRBs). Our analysis reveals a transition redshift from deceleration to acceleration at $z_{\mathrm{tr}}=0.69$ and a present-day deceleration parameter value of $q_0=-0.64$. The model supports a dynamical scalar field interpretation, with an equation of state parameter satisfying $-1<{\omega }_0^{\varphi }<0$, consistent with quintessence behavior, and signaling a deviation from the $\mathrm{\Lambda }$. While the model aligns closely with the Lambda Cold Dark Matter scenario at lower redshifts ($z\lesssim 0.65$), notable departures emerge at higher redshifts ($z\gtrsim 0.65$), offering a potential window into modified early-time cosmology. Furthermore, the evolution of key cosmographic quantities such as energy density ${\rho }^{\varphi }$, pressure $p^{\varphi }$, and the scalar field equation of state highlights the robustness of scalar field frameworks in describing dark energy phenomenology. Importantly, our results indicate a slightly higher value of the Hubble constant $H_0$ for specific data combinations, suggesting that the model may provide a partial resolution of the current $H_0$ tension. Full article

We consider constraints on the Hubble parameter $H_0$ and the matter density parameter ${\mathrm{\Omega }}_{\mathrm{M}}$ from the following: (i) the age of the Universe based on old stars and stellar populations in the Galactic disc and halo; (ii) the turnover scale in the matter power spectrum, which tells us the cosmological horizon at the epoch of matter-radiation equality; and (iii) the shape of the expansion history from supernovae (SNe) and baryon acoustic oscillations (BAOs) with no absolute calibration of either, a technique known as uncalibrated cosmic standards (UCS). A narrow region is consistent with all three constraints just outside their $1\sigma$ uncertainties. Although this region is defined by techniques unrelated to the physics of recombination and the sound horizon then, the standard Planck fit to the CMB anisotropies falls precisely in this region. This concordance argues against early-time explanations for the anomalously high local estimate of $H_0$ (the ‘Hubble tension’), which can only be reconciled with the age constraint at an implausibly low ${\mathrm{\Omega }}_{\mathrm{M}}$. We suggest instead that outflow from the local KBC supervoid inflates redshifts in the nearby universe and, thus, the apparent local $H_0$. Given the difficulties with solutions in the early universe, we argue that the most promising alternative to a local void is a modification to the expansion history at late times, perhaps due to a changing dark energy density. Full article

We investigate a combined conservative field, in which classical gravitational and electrostatic sources also exhibit mutual interactions. Hitherto neglected, the coupling between mass and charge may be necessary for constructing a unified conservative force field generated by a single underlying source. We determine the coupling constant of the cross-field components as the geometric mean (G-M) of Newton’s G and Coulomb’s K constants, in both SI units and dimensionless form. Consequently, for two identical objects, the cross-force ($F_{\times }$) is the G-M of the familiar Newton ($F_{\mathrm{g}}$) and Coulomb ($F_{\mathrm{e}}$) forces, so that $F_{\times }=\sqrt{F_{\mathrm{g}}{F}_{\mathrm{e}}}$, where $F_{\mathrm{g}}\ll F_{\times }\ll F_{\mathrm{e}}$. Remarkably, such cross-forces should be measurable in torsion balance experiments involving a suspended neutral mass interacting with a partially ionized gas. Furthermore, we apply our new formulation to estimate the dimensionless amplitude $\parallel {\mathcal{h}}_{\alpha \beta }^{\mathrm{TT}}\parallel$ of gravitational waves that are emitted by inspiraling Reissner–Nordström (RN) black hole binaries, expressed in terms of ratios of the four fundamental lengths of the problem: the distance to the binary D, the binary separation R, the Schwarzschild radius $R_S\propto 2M$ of mass M, and the RN charge (Q) length scale $L_Q\propto 2Q$. In this classical setting with speeds much lower than the speed of light c in vacuum, the surprising appearance of the maximum relativistic tension force $F_{\max }=c^4/\left(4G\right)$ is duly noted. Full article

In this work, we investigate how a change in the sound horizon due to inflation may affect the value of $H_0$. Performing an analysis using the measurements of BAO, SN Ia, $H\left(z\right)$, CMB, and the local $H_0$, we show that the modification in the sound horizon brings the nearly 5$\sigma$ tension in $H_0$ estimates to approximately $1\sigma$. The overall fit is also improved as compared with the standard calculation of $r_s$. These findings highlight the importance of early-universe physics in resolving late-time cosmological tensions. Full article

The Two-Measure Theory (TMT) has been developing since 1998 and has yielded a number of highly interesting results, including those not realized in traditional field theory models. The most important advantage of TMT as an alternative theory is that, under the conditions under which all classical tests of general relativity are performed, TMT models are able to accurately reproduce Einstein’s general relativity. Despite this, TMT is still often perceived as something too exotic to be relevant to reality. In fact, the fundamental idea underlying TMT seems undeniable: if we truly believe in the effectiveness of mathematics in studying nature, we must agree that there must be a correspondence between the fundamental laws of nature and the structure of the mathematical apparatus necessary to adequately describe them. It then turns out that there is no reason to ignore the volume measure existing on the differentiable manifold on which the theory of gravity and matter fields is built. This idea has far-reaching implications. The goals of this paper are (1) to provide a clear mathematical and conceptual justification for TMT and (2) to collect in a single article some of the main results of TMT obtained over the past 25 years. Full article

In this paper we present a brief review of extended general relativity in four dimensions and solve versions of the extended equations for the case of static spherical symmetry in various contexts, for a previously studied Lagrangian. The exterior vacuum yields a Schwarzschild solution with an additional scalar field potential that falls off logarithmically, the latter essentially an inverse square force. That is probably not adequate as a dark matter force, but might contribute. When a constant density field of ions holds sway in the exterior, a solution identical to the cosmological constant extension of Schwarzschild occurs, together with a scalar field potential declining as $r^{-3/2}$, however it is not asymptotically flat. An inverse square declining distribution of ionic material, according to perturbation theory, results in an additional linear gravity potential that would provide further attraction in the gravity term. A limited exact solution in the same case yields a cubic equation with a Schwarzschild solution, corresponding to $A=0$, and two MOND-like possible potentials, one vanishing at infinity, but a better solution must be found. The approximate solution is complex (one of many) and the system requires further study. Ionic matter is ubiquitous in the universe and provides a source for the scalar field, which suggests that the extended Einstein equations could be of utility in the dark matter problem, provided such an electromagnetic scalar force could be found and differentiated from the usual, far stronger electromagnetic forces. Further, it’s possible that the strong photon flux outside stars might have an influence, and is under current investigation. These calculations show that extending the concept of curvature and working in four dimensions with larger operators may bring new tools to the study of physics and unified field theories. Full article

We present a comprehensive quantum field theoretical analysis of graviton self-energy and mass generation in 3+1 dimensional BTZ black hole spacetime, incorporating axion interactions within the framework of dark matter theory. Using a novel mathematical approach based on ultrahyperfunctions, generalizations of Schwartz tempered distributions to the complex plane, we derive exact quantum relativistic expressions for graviton and axion self-energies without requiring ad hoc regularization procedures. Our approach extends the Gupta–Feynman quantization framework to BTZ gravity while introducing a new constraint that eliminates unitarity violations inherent in previous formulations, thereby avoiding the need for ghost fields. Through systematic application of generalized Feynman parameters, we evaluate both bradyonic and tachyonic graviton modes, revealing distinct quantum correction patterns that depend critically on momentum, energy, and mass parameters. Key findings include (1) natural graviton mass generation through cosmological constant interactions, yielding $m^2=2\left|\mathsf{\Lambda }\right|/\kappa (1-\kappa )$; (2) qualitatively different quantum behaviors between bradyonic and tachyonic modes, with bradyonic corrections reaching amplitudes 6 times larger than their tachyonic counterparts; (3) the discovery of momentum-dependent quantum dissipation effects that provide natural ultraviolet regulation; and (4) the first explicit analytical expressions and graphical representations for 17 distinct graviton self-energy contributions. The ultrahyperfunction formalism proves essential for handling the non-renormalizable nature of the theory, providing mathematically rigorous treatment of highly singular integrals while maintaining Lorentz invariance. Our results suggest observable consequences in gravitational wave propagation through frequency-dependent dispersive effects and modifications to black hole thermodynamics, potentially bridging theoretical quantum gravity with experimental constraints. Full article

Modified gravity theories with a nonminimal coupling between curvature and matter offer a compelling alternative to dark energy and dark matter by introducing an explicit interaction between matter and curvature invariants. Two of the main consequences of such an interaction are the emergence of an additional force and the non-conservation of the energy–momentum tensor, which can be interpreted as an energy exchange between matter and geometry. By adopting this interpretation, one can then take advantage of many different approaches in order to investigate the phenomenon of gravitationally induced particle creation. One of these approaches relies on the so-called irreversible thermodynamics of open systems formalism. By considering the scalar–tensor formulation of one of these theories, we derive the corresponding particle creation rate, creation pressure, and entropy production, demonstrating that irreversible particle creation can drive a late-time de Sitter acceleration through a negative creation pressure, providing a natural alternative to the cosmological constant. Furthermore, we demonstrate that the generalized second law of thermodynamics holds: the total entropy, from both the apparent horizon and enclosed matter, increases monotonically and saturates in the de Sitter phase, imposing constraints on the allowed particle production dynamics. Furthermore, we present brief reviews of other theoretical descriptions of matter creation processes. Specifically, we consider approaches based on the Boltzmann equation and quantum-based aspects and discuss the generalization of the Klein–Gordon equation, as well as the problem of its quantization in time-varying gravitational fields. Hence, gravitational theories with nonminimal curvature–matter couplings present a unified and testable framework, connecting high-energy gravitational physics with cosmological evolution and, possibly, quantum gravity, while remaining consistent with local tests through suitable coupling functions and screening mechanisms. Full article

In this investigation, we explore previously unknown relations between natural constants by taking the following steps: (1) We discard Dirac’s constant ℏ from the universal man-made constants of physics, which we redefine in terms of Planck’s constant h. (2) Working in the SI system of units, we determine Newton’s gravitational constant G from Boltzmann’s constant $k_{\mathrm{B}}$ and the elementary charge e, recognizing the entropy of matter as their common underlying characteristic. (3) By comparing the mass of 1 mole of electrons to the h-defined Planck mass $M_{\mathrm{P}}$, we deduce nature’s own molar constant ($\simeq$0.1 mol) that contains a ‘reduced Avogadro number’ ${\aleph }_{\mathrm{A}}=N_{\mathrm{A}}/f_{\mathrm{A}}$ of particles, where $N_{\mathrm{A}}$ is Avogadro’s number and $f_{\mathrm{A}}\simeq 10$ is the associated Avogadro factor. (4) From the new effective gravitational constant $G_{★}\equiv 4\pi {\epsilon }_{0}G$, where ${\epsilon }_0$ is the vacuum permittivity, we obtain MOND’s universal constant ${\mathcal{A}}_0$ and its critical acceleration $a_0$, recognizing the Newtonian source of gravity as the common underlying characteristic and repudiating the need for a principle of equivalence of masses. (5) We derive the gravitational coupling constant ${\mathsf{\alpha }}_{\mathrm{g}}$ solely from ${\aleph }_{\mathrm{A}}$. (6) We adopt the measured value of the h-defined fine-structure constant (FSC) $\mathsf{\alpha }$ and the value of ${\mathsf{\alpha }}_{\mathrm{g}}$ (or, equivalently, nature’s ${\aleph }_{\mathrm{A}}$), and we determine the relative ratio ${\mathsf{\beta }}_{\mathrm{g}}={\mathsf{\alpha }}_{\mathrm{g}}/\mathsf{\alpha }$ precise to 10 significant digits. (7) We derive the relative strong ratio ${\mathsf{\beta }}_{\mathrm{s}}={\mathsf{\alpha }}_{\mathrm{s}}/\mathsf{\alpha }$ directly from the Avogadro factor $f_{\mathrm{A}}$. (8) We determine the coupling constants of weak and strong interactions (${\mathsf{\alpha }}_{\mathrm{w}}$ and ${\mathsf{\alpha }}_{\mathrm{s}}$, respectively) in terms of the FSC $\mathsf{\alpha }$. (9) The relation ${\mathsf{\alpha }}_{\mathrm{w}}=\sqrt{\mathsf{\alpha }}$ leads to a determination of the mass of the W boson $m_{\mathrm{W}}$ from the measured values of $\mathsf{\alpha }$ and the reduced Fermi constant $G_{\mathrm{F}}^0$. (10) Using the Planck mass as a principal constant ($M_{\mathrm{P}}={\aleph }_{\mathrm{A}}{m}_{\mathrm{e}}$, where $m_{\mathrm{e}}$ is the electron mass), we obtain new classical definitions of $h,\mathsf{\alpha }$, and the Compton radius $r_{\mathrm{c}}$; and we reformulate in a transparent, geometrically clear way several important QED equations, as well as the extended Planck system of units itself. We discuss the implications of these results, and we pave a way forward in exploring the unification of the fundamental forces of nature. Full article

If the recent acceleration phase of the expanding Universe is driven by a cosmologicalconstant the Universe is future-eternal with a few far reaching ramifications and disturbing consequences. We demonstrate with a non-ΛCDM cosmological model, that is nearly identical to the standard cosmological model insofar observations of our past are concerned—but otherwise has an effective cosmic time cutoff—that under certain plausible assumptions observers will virtually always find themselves at or near the end of time (EOT) terminal point, where H₀η₀ = π, and H₀ and η₀ are the present day expansion rate and the conformal time, respectively. Assuming a locally flat ΛCDM model for concreteness (but with a global terminal point which is with an overwhelming probability the present time) such observers will invariably infer that the energy densities associated with the cosmological constant, Λ, and non-relativistic (NR) matter constitute 67.5% and 32.5%, respectively, of the cosmic energy budget at present, which lie well within the 2σ confidence level of the concordance 68.5% and 31.5% values. This addresses the Cosmic Coincidence Problem associated with Λ. Future high-precision cosmological probes will be able to break the observational degeneracy between the proposed model and flat ΛCDM. A few additional implications of the proposed model are discussed as well. Full article

Recently, a link between gravitational tension (GT) and energy density via the Kretschmann scalar (KS) was proposed to construct regular black holes (RBHs) in pure Lovelock (PL) gravity. However, including a negative cosmological constant in PL gravity leads to a curvature singularity. Here, we choose the coupling constants such that the Lovelock equations admit an n-fold degenerate AdS vacuum (LnFDGS), allowing us to construct an RBH with $\Lambda <0$, where the energy density is analogous to the previously mentioned model. To achieve this, we propose alternative definitions for both the KS and GT. We find that, for mass parameter values greater than the extremal value $M_{\min }$, our RBH solution becomes indistinguishable from the AdS vacuum black hole from inside the event horizon out to infinity. At small scales, quantum effects modify the geometry and thermodynamics, removing the singularity. Furthermore, due to the lack of analytical relationships between the event horizon, photon sphere, and shadow in LnFDGS, we propose a numerical method to represent these quantities. Full article

The formation and evolution of galaxies and other astrophysical objects have become of great interest, especially since the launch of the James Webb Space Telescope in 2021. The mass, size, and density of objects in the early universe appear to be drastically different from those predicted by the standard cosmology—the $\mathsf{\Lambda }$CDM model. This work shows that the mass–size–density evolution is not surprising when we use the CCC+TL cosmology, which is based on the concepts of covarying coupling constants in an expanding universe and the tired light effect contributing to the observed redshift. This model is consistent with supernovae Pantheon+ data, the angular size of the cosmic dawn galaxies, BAO, CMB sound horizon, galaxy formation time scales, time dilation, galaxy rotation curves, etc., and does not have the coincidence problem. The effective radii $r_e$ of the objects are larger in the new model by $r_e\propto {\left(1+z\right)}^{0.93}$. Thus, the object size evolution in different studies, estimated as $r_e\propto {\left(1+z\right)}^s$ with $s=-1.0$ ± $0.3$, is modified to $r_e\propto {\left(1+z\right)}^{s+0.93}$, the dynamical mass by ${\left(1+z\right)}^{0.93},$ and number density by ${\left(1+z\right)}^{-2.80}$. The luminosity modification increases slowly with $z$ to 1.8 at $z=20$. Thus, the stellar mass increase is modest, and the luminosity and stellar density decrease are mainly due to the larger object size in the new model. Since the aging of the universe is stretched in the new model, its temporal evolution is much slower (e.g., at $z=10$, the age is about a dex longer); stars, black holes, and galaxies do not have to form at unrealistic rates. Full article

This paper presents a systematic literature review focusing on the application of machine learning techniques for deriving observational constraints in cosmology. The goal is to evaluate and synthesize existing research to identify effective methodologies, highlight gaps, and propose future research directions. Our review identifies several key findings: (1) Various machine learning techniques, including Bayesian neural networks, Gaussian processes, and deep learning models, have been applied to cosmological data analysis, improving parameter estimation and handling large datasets. However, models achieving significant computational speedups often exhibit worse confidence regions compared to traditional methods, emphasizing the need for future research to enhance both efficiency and measurement precision. (2) Traditional cosmological methods, such as those using Type Ia Supernovae, baryon acoustic oscillations, and cosmic microwave background data, remain fundamental, but most studies focus narrowly on specific datasets. We recommend broader dataset usage to fully validate alternative cosmological models. (3) The reviewed studies mainly address the $H_0$ tension, leaving other cosmological challenges—such as the cosmological constant problem, warm dark matter, phantom dark energy, and others—unexplored. (4) Hybrid methodologies combining machine learning with Markov chain Monte Carlo offer promising results, particularly when machine learning techniques are used to solve differential equations, such as Einstein Boltzmann solvers, prior to Markov chain Monte Carlo models, accelerating computations while maintaining precision. (5) There is a significant need for standardized evaluation criteria and methodologies, as variability in training processes and experimental setups complicates result comparability and reproducibility. (6) Our findings confirm that deep learning models outperform traditional machine learning methods for complex, high-dimensional datasets, underscoring the importance of clear guidelines to determine when the added complexity of learning models is warranted. Full article