Search Results (33)

We develop the geometry of events in a deformable cellular spacetime, extending our earlier cellular-spaces framework from cellular complexes to cellular events complexes. The framework operates within the conformal class of Minkowski space; in four dimensions, this is the vanishing-Weyl-tensor sector, which excludes Schwarzschild, Kerr, and gravitational-wave spacetimes. The framework treats integer counts of cell crossings as the primitive geometric data: spatial separation between events is the shortest count of face-adjacent cells; temporal separation is the cell-crossing count of a reference light pulse. Newton’s universal clock is replaced by an operational one: the temporal count distance is the ratio of cell length to the speed of light through a cell, and because both quantities are invariants of the co-deformation, the temporal count is itself an invariant: temporal separation is operationally measured via light-pulse counts rather than posited as an external coordinate. Under the co-deformation principle, a single positive scalar field $\rho$ (cell density) controls both the rod length and the clock period. We prove six results, all expressed in terms of counts on the cellular events complex, with a smooth conformally flat metric $\tilde{g}=e^{2\phi }\eta$ ($\phi =-\frac{1}{3}ln\rho$) appearing only as the comparison/calibration object for convergence statements. First, the scalar curvature of the smooth comparison metric is the closed-form differential operator $\tilde{R}=2\square \rho /{\rho }^{1/3}-(8/3){(\partial \rho )}^2/{\rho }^{4/3}$. Second, the volume of a small Alexandrov interval admits an explicit asymptotic expansion in the interval height T, with leading correction $Q(m,u)T^2$ involving an anisotropic invariant at the midpoint m. Third, Q is irreducible to scalar and Ricci-directional invariants alone; the explicit decomposition $Q=\frac{1}{45}\tilde{R}+\frac{1}{5}{\tilde{R}}_{uu}+\frac{1}{2}\mathcal{J}$ exhibits a third independent invariant $\mathcal{J}(m,u)={(u·\partial )}^2\phi \left(m\right)$ as new structural content of the Lorentzian diagnostic. Fourth, the discrete-to-continuum convergence of counts on the cellular events complex yields a counts-only curvature estimator with rate $O\left(\sqrt{a}\right)$ at the joint scaling $T\asymp \sqrt{a}$. Fifth, the smooth comparison metric itself is reconstructible from counts on the discrete complex at rate $O\left(a\right)$: the conformally flat Lorentzian geometry is uniquely determined, up to background Minkowski calibration, by the cellular events complex. Sixth, a finite collection of Alexandrov-interval volume measurements at a fixed midpoint suffices to recover the full local curvature data $\{\tilde{R}\left(m\right),{\tilde{R}}_{\mu \nu }\left(m\right),\mathcal{J}(m,u)\}$ at rate $O\left(\sqrt{a}\right)$ (curvature spectroscopy); and the temporal light-tick count $\lambda$ is essential in a precise sense—there exist conformally flat Lorentzian geometries indistinguishable on every spatial slice by the earlier spatial-only diagnostic but distinguished at the origin by the events-space directional invariant. The framework’s scope is the conformal class of Minkowski: flat FLRW in conformal time, leading-order weak-field gravity, and 2D gravity. This paper is a mathematical contribution to discrete-to-continuum geometry on cellular events complexes; it is not a physical theory of gravity. Full article

The present paper is devoted to the study of Lorentzian spacetimes endowed with the pseudo $W_2$-curvature tensor. We investigate the geometric and symmetry properties of pseudo $W_2$-flat spacetimes and establish several results concerning their curvature structure and associated energy–momentum tensors. It is shown that a pseudo $W_2$-flat spacetime is a spacetime of constant curvature under suitable conditions on the defining parameters of the pseudo $W_2$-curvature tensor. Further, for a spacetime satisfying Einstein’s field equation with vanishing pseudo $W_2$-curvature tensor, it is proved that a vector field generates a matter collineation if and only if it is a Killing vector field. We also establish that the Lie inheritance property of the energy–momentum tensor is equivalent to the existence of a conformal Killing vector field. Moreover, it is shown that if the energy–momentum tensor is of Codazzi type, then the pseudo $W_2$-curvature tensor is divergence-free. To illustrate the obtained results, two explicit Lorentzian spacetime models are examined in detail, namely an isotropic warped spacetime and an FLRW-type exponential (de Sitter) spacetime. For each model, the metric structure, curvature tensors, Ricci operator, scalar curvature, and pseudo $W_2$-flatness condition are verified explicitly. These examples provide concrete realizations of the theoretical results and demonstrate the significance of the pseudo $W_2$-curvature tensor in the geometric study of Lorentzian manifolds and general relativity. Full article

Applications of Parametrized Relativistic Quantum Theory (PRQT) in curved spacetime are considered here. PRQT in curved spacetime is applied to the motion of free scalar particles in expanding universe metrics, including a generalized expanding universe (EU) metric and the Friedmann–Lemaître–Robertson–Walker (FLRW) metric. Governing equations are derived and solved through separation of variables. In addition, modern observational parameters and a rescaled Friedmann equation are used to estimate the age of the universe. Implications for cosmological models are discussed. Full article

We present a comprehensive general relativistic analysis of the Lemaître–Tolman–Bondi (LTB) metric, incorporating a cosmological constant $\mathrm{\Lambda }$ and a central pointlike mass $M_{\mathrm{d}}$ at the geometric origin. Within this framework, $M_{\mathrm{d}}$ is identified as the material source of dark matter in cosmology, yielding a scale-dependent total matter–density parameter ${\mathrm{\Omega }}_{\mathrm{m}}\left(L\right)$ characterized by an $L^{-3}$ decay of its dark component ${\mathrm{\Omega }}_{\mathrm{d}}\left(L\right)$. We demonstrate that the Hubble and $S_8$ tensions are not independent anomalies but interconnected consequences of spacetime inhomogeneity. These discrepancies arise from a combination of physical and methodological factors: the probing of radial gradients at different characteristic scales and the subsequent interpretation of these data through a global FLRW template. This approach, compounded by the practice of isotropic sky averaging, masks the underlying LTB geometry and converts the physical variation of the manifold into the observed cosmological tensions. Our framework provides a self-consistent geometric explanation for current anomalies while preserving the Copernican principle, identifying the crisis in cosmology as arising from the application of homogeneous models to a manifold characterized by radial gradients and scale-dependent dynamics, where the observer and probes reside within the same inhomogeneous regime. Full article

We show that the FLRW metric, modified to include interrelated variation in the speed of light and gravitational constants, leads to Friedmann equations containing terms that behave like dark matter and dark energy without the cosmological constant. When we permit tired light (TL) to contribute to the redshift due to the expanding universe, thus defined by covarying coupling constants (CCCs), the resulting CCC+TL model has a critical density that is just enough to account for the baryon matter in the universe. The CCC+TL cosmology model is consistent with all of the observations that we had the time and the resources to study, including BAOs (baryon acoustic oscillations), the CMB (cosmic microwave background) sound horizon angular size, the time dilation effect, galaxy formation time scales at cosmic dawn, galaxy rotation curves, gravitational lensing, galaxy cluster and ultra-faint dwarf galaxy dynamics, and the mass, size, density, and luminosity evolution of galaxies. We briefly review them in this paper. Additionally, the new model does not suffer from the coincidence problem of the ΛCDM model and complies with the recent DESI findings of an increasing dark energy density with redshift. We present the fundamentals of the CCC+TL model and discuss its applications to some decisive observations. We have considered temporal variation in the constant for cosmological studies and their spherically symmetric variation in astrophysical situations. We conclude that the illusion of dark matter and dark energy in cosmological and astrophysical observations originates from CCC. Full article

The present work discusses the birth of the Universe via quantum tunneling through a potential barrier, based on quantum cosmology, taking a running cosmological constant into account. We consider the Friedmann–Lemaître–Robertson–Walker (FLRW) metric with positively curved spatial sections ($k=1$) and the matter’s content is a dust perfect fluid. The model was quantized by the Dirac formalism, leading to a Wheeler–DeWitt equation. We solve that equation both numerically and using a WKB approximation. We study the behavior of tunneling probabilities $T{P}_{WKB}$ and $T{P}_{int}$ by varying the energy E of the dust perfect fluid, the phenomenological parameter $\nu$, the present value of the Hubble function $H_0$, and the constant energy density ${\rho }_{\Lambda }^0$, with the last three parameters all being associated with the running cosmological constant. We observe that both tunneling probabilities, $T{P}_{WKB}$ and $T{P}_{int}$, decrease as one increases $\nu$. We also note that $T{P}_{WKB}$ and $T{P}_{int}$ grow as E increases, indicating that the Universe is more likely to be born with higher dust energy E values. The same is observed for the parameter ${\rho }_{\Lambda }^0$, that is, $T{P}_{WKB}$ and $T{P}_{int}$ are larger for higher values of ${\rho }_{\Lambda }^0$. Finally, the tunneling probabilities decrease as one increases the value of $H_0$. Therefore, the best conditions for the Universe to be born, in the present model, would be to have the highest possible values for E and $\Lambda$ and the lowest possible values for $\nu$ and $H_0$. Full article

We investigate the behaviour of photons in Riemann spacetime, focusing on how their velocity and energy are affected by cosmic expansion. Specifically, we examine the differences in energy conservation depending on the cosmological model. Our findings indicate that photons exhibit fundamentally different behaviour based on the chosen metric. In the standard $\Lambda$CDM model, which relies on the Friedmann–Lemaître–Robertson–Walker (FLRW) metric, the energy conservation law for redshifted photons is violated. However, in a cosmological model based on the conformal cosmology (CC) metric, this law remains valid. The CC metric offers additional advantages, as it accurately reproduces the cosmological redshift, cosmic time dilation observed in Type Ia supernova light curves, and flat galaxy rotation curves without requiring the introduction of dark matter. These findings underscore the potential significance of the CC metric in cosmological applications. Full article

In this article, we investigate the influence of viscosity on the evolution of the cosmos within the framework of the newly proposed $f(Q,L_m)$ gravity. We have considered a linear functional form $f(Q,L_m)=\alpha Q+\beta L_m$ with a bulk viscous coefficient $\zeta ={\zeta }_0+{\zeta }_{1}H$ for our analysis and obtained exact solutions to the field equations associated with a flat FLRW metric. In addition, we utilized Cosmic Chronometers (CC), CC + BAO, CC + BAO + GRB, and GRB data samples to determine the constrained values of independent parameters in the derived exact solution. The likelihood function and the Markov Chain Monte Carlo (MCMC) sampling technique are combined to yield the posterior probability using Bayesian statistical methods. Furthermore, by comparing our results with the standard cosmological model, we found that our considered model supports the acceleration of the universe in late time. Full article

Wormholes are non-trivial topological structures that arise as exact solutions to Einstein’s field equations, theoretically connecting distinct regions of spacetime via a throat-like geometry. While static traversable wormholes necessarily require exotic matter that violates the classical energy conditions, subsequent studies have sought to minimize such violations by introducing time-dependent geometries embedded within cosmological backgrounds. This review provides a comprehensive survey of evolving wormhole solutions, emphasizing their formulation within both general relativity and alternative theories of gravity. We explore key developments in the construction of non-static wormhole spacetimes, including those conformally related to static solutions, as well as dynamically evolving geometries influenced by scalar fields. Particular attention is given to the wormholes embedded into Friedmann–Lemaître–Robertson–Walker (FLRW) universes and de Sitter backgrounds, where the interplay between the cosmic expansion and wormhole dynamics is analyzed. We also examine the role of modified gravity theories, especially in hybrid metric–Palatini gravity, which enable the realization of traversable wormholes supported by effective stress–energy tensors that do not violate the null or weak energy conditions. By systematically analyzing a wide range of time-dependent wormhole solutions, this review identifies the specific geometric and physical conditions under which wormholes can evolve consistently with null and weak energy conditions. These findings clarify how such configurations can be naturally integrated into cosmological models governed by general relativity or modified gravity, thereby contributing to a deeper theoretical understanding of localized spacetime structures in an expanding universe. Full article

Papapetrou showed that the covariant derivative of a Killing vector field satisfies Maxwell’s equations in vacuum. Papapetrou’s result is extended, in this article, and it is shown that the covariant derivative of a Killing vector field satisfies Maxwell’s equations in non-vacuum backgrounds as well if one allows electromagnetic currents of purely geometric origin. It is then postulated that every Killing vector field gives rise to a physical electromagnetic field and, in a non-vacuum background, a physical electromagnetic current—hereafter called Killing electromagnetic field and Killing electromagnetic current, respectively. It is shown that the Killing electromagnetic field of the flat FLRW (Friedmann–Lema$\hat{\mathrm{i}}$tre–Robertson–Walker) universe comprises a Killing magnetic field and a rotational Killing electric field; an upper bound on the Killing magnetic field is derived, and it is found that the upper bound is consistent with the current observational bounds on the cosmic magnetic field. Next, the time-like Killing vector of the Schwarzschild spacetime is shown to give rise to a radial Killing electric field. It is also shown that in the weak field regime—and far from the matter distribution—the back reaction of the radial Killing electric field changes the Schwarzschild metric to the Reissner–Nordström metric, establishing a partial converse of Wald’s result. Drawing upon Rainich’s work on Rainich–Riemann manifolds, the etiological question of how a physical electromagnetic field can arise out of geometry is discussed; it is also argued that detection of the Killing electric field of flat FLRW spacetime may be within the current experimental reach. Finally, this article discusses the relevance of Killing electromagnetic currents and the aforementioned transmutation of Schwarzschild spacetime to Reissner–Nordstrom spacetime, to Misner and Wheeler’s program of realizing “charge without charge”. Full article

The cosmic time dilation observed in Type Ia supernova light curves suggests that the passage of cosmic time varies throughout the evolution of the Universe. This observation implies that the rate of proper time is not constant, as assumed in the standard FLRW metric, but instead is time-dependent. Consequently, the commonly used FLRW metric should be replaced by a more general framework, known as the Conformal Cosmology (CC) metric, to properly account for cosmic time dilation. The CC metric incorporates both spatial expansion and time dilation during cosmic evolution. As a result, it is necessary to distinguish between comoving and proper (physical) time, similar to the distinction made between comoving and proper distances. In addition to successfully explaining cosmic time dilation, the CC metric offers several further advantages: (1) it preserves Lorentz invariance, (2) it maintains the form of Maxwell’s equations as in Minkowski spacetime, (3) it eliminates the need for dark matter and dark energy in the Friedmann equations, and (4) it successfully predicts the expansion and morphology of spiral galaxies in agreement with observations. Full article

We perform observational confrontation and cosmographic analysis of $f(T,T_G)$ gravity and cosmology. This higher-order torsional gravity is based on both the torsion scalar, as well as on the teleparallel equivalent of the Gauss–Bonnet combination, and gives rise to an effective dark-energy sector which depends on the extra torsion contributions. We employ observational data from the Hubble function and supernova Type Ia Pantheon datasets, applying a Markov chain Monte Carlo sampling technique, and we provide the iso-likelihood contours, as well as the best-fit values for the parameters of the power-law model, an ansatz which is expected to be a good approximation of most realistic deviations from general relativity. Additionally, we reconstruct the effective dark-energy equation-of-state parameter, which exhibits a quintessence-like behavior, while in the future the Universe enters into the phantom regime, before it tends asymptotically to the cosmological constant value. Furthermore, we perform a detailed cosmographic analysis, examining the deceleration, jerk, snap, and lerk parameters, showing that the transition to acceleration occurs in the redshift range $0.52\le z_{tr}\le 0.89$, as well as the preference of the scenario for quintessence-like behavior. Finally, we apply the Om diagnostic analysis to cross-verify the behavior of the obtained model. Full article

Considering the Friedmann–Lemaître–Robertson–Walker (FLRW) metric and the Einstein scalar field system as an underlying gravitational model to construct fractional cosmological models has interesting implications in both classical and quantum regimes. Regarding the former, we just review the most fundamental approach to establishing an extended cosmological model. We demonstrate that employing new methodologies allows us to obtain exact solutions. Despite the corresponding standard models, we cannot use any arbitrary scalar potentials; instead, it is determined from solving three independent fractional field equations. This article concludes with an overview of a fractional quantum/semi-classical model that provides an inflationary scenario. Full article

We analyze the transformation of a very broad class of metrics that can be expressed in terms of static coordinates. Starting from a general ansatz, we obtain a relation for the parameters in which one can impose further symmetries or restrictions. One of the simplest restrictions leads to FLRW cases, while transforming from the initial static to other static-type coordinates can lead to near horizon coordinates, Wheeler–Regge, and isotropic coordinates, among others. As less restrictive cases, we show an indirect route for obtaining Kruskal–Szekeres within this approach, as well as Lemaître coordinates. We use Schwarzschild spacetime as a prototype for testing the procedure in individual cases. However, application to other spacetimes, such as de-Sitter, Reissner–Nordström, and Schwarzschild de Sitter, can be readily generalized. Full article

We construct and examine a holonomy-corrected chiral fields model of cosmological relevance. Specifically, we holonomize the Hamiltonian corresponding to a quintom field scenario with additional kinetic interaction (governed by the constant chiral metric, $m_{ab}$) on a flat FLRW background and contrast the resulting model with the corresponding purely classical system. In particular, it is shown that the single LQC bouncing stage is ensured to be realized, provided the full chiral kinetic energy function does not change sign during evolution. (As preparation, a particularly simple k-essence field is examined within the effective LQC scheme; some exact solutions are obtained in the process.) Additionally, under the said assumption, it is established that the landmark bouncing mechanism of standard (effective) LQC is still guaranteed to be featured even when taking any finite number of fields ${\varphi }^1,\dots {\varphi }^m$ and $m_{ab}$ to be dependent on such fields (the particular zero-potential case corresponding to a family of simple purely kinetic k-essence multi-field cosmology models). Full article