Search Results (40)

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

In this paper, we extend the study of contravariant Einstein-like metrics to Poisson doubly warped product manifolds (PDWPMs). We derive the necessary and sufficient conditions under which the base and fiber manifolds of a PDWPM inherit Einstein-like structures from the total space. As applications, we construct Einstein-like Poisson doubly warped product structures belonging to classes $\mathcal{A}$, $\mathcal{B}$, and $\mathcal{P}$ in various spacetime models, including generalizations of Reissner–Nordström, standard static, and Robertson–Walker spacetimes. 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

We present a review of recent developments in cosmological models based on Finsler geometry, as well as geometric extensions of general relativity formulated within this framework. Finsler geometry generalizes Riemannian geometry by allowing the metric tensor to depend not only on position but also on an additional internal degree of freedom, typically represented by a vector field at each point of the spacetime manifold. We examine in detail the possibility that Finsler-type geometries can describe the physical properties of the gravitational interaction, as well as the cosmological dynamics. In particular, we present and review the implications of a particular implementation of Finsler geometry, based on the Barthel connection, and of the $(\alpha ,\beta )$ geometries, where $\alpha$ is a Riemannian metric, and $\beta$ is a one-form. For a specific construction of the deviation part $\beta$, in these classes of geometries, the Barthel connection coincides with the Levi–Civita connection of the associated Riemann metric. We review the properties of the gravitational field, and of the cosmological evolution in three types of geometries: the Barthel–Randers geometry, in which the Finsler metric function F is given by $F=\alpha +\beta$, in the Barthel–Kropina geometry, with $F={\alpha }^2/\beta$, and in the conformally transformed Barthel–Kropina geometry, respectively. After a brief presentation of the mathematical foundations of the Finslerian-type modified gravity theories, the generalized Friedmann equations in these geometries are written down by considering that the background Riemannian metric in the Randers and Kropina line elements is of Friedmann–Lemaitre–Robertson–Walker type. The matter energy balance equations are also presented, and they are interpreted from the point of view of the thermodynamics of irreversible processes in the presence of particle creation. We investigate the cosmological properties of the Barthel–Randers and Barthel–Kropina cosmological models in detail. In these scenarios, the additional geometric terms arising from the Finslerian structure can be interpreted as an effective geometric dark energy component, capable of generating an effective cosmological constant. Several cosmological solutions—both analytical and numerical—are obtained and compared against observational datasets, including Cosmic Chronometers, Type Ia Supernovae, and Baryon Acoustic Oscillations, using a Markov Chain Monte Carlo (MCMC) analysis. A direct comparison with the standard $\Lambda$CDM model is also carried out. The results indicate that Finslerian cosmological models provide a satisfactory fit to the observational data, suggesting they represent a viable alternative to the standard cosmological model based on general relativity. Full article

In the present article, we classify conformally flat weakly Ricci-symmetric space-times and obtain that they represent Robertson–Walker space-times. Furthermore, we provethat a Ricci-recurrent weakly Ricci-symmetric space-time is static and a Ricci-semi-symmetric weakly Ricci-symmetric space-time does not exist. Further, we acquire the conditions under which a weakly Ricci-symmetric twisted space-time becomes a generalized Robertson–Walker space-time. Also, we examine the effect of conformally flat weakly Ricci-symmetric space-time solutions in $f(R,G)$ gravity by considering two models, and we see that the null, weak and strong energy conditions are verified, but the dominant energy condition fails, which is also consistent with present observational studies that reveal the universe is expanding. Finally, we apply the flat Friedmann–Robertson–Walker metric to deduce a relation between deceleration, jerk and snap parameters. Full article

The aim of this work is to demonstrate that all linear derivatives of the tensor algebra over a smooth manifold M can be viewed as specific cases of a broader concept—the operation of derivation. This approach reveals the universal role of differentiation, which simplifies and generalizes the study of tensor derivatives, making it a powerful tool in Differential Geometry and related fields. To perform this, the generic derivative is introduced, which is defined in terms of the quantities $Q_k^{\left(i\right)}\left(X\right)$. Subsequently, the transformation law of these quantities is determined by the requirement that the generic derivative of a tensor is a tensor. The quantities $Q_k^{\left(i\right)}\left(X\right)$ and their transformation law define a specific geometric object on M, and consequently, a geometric structure on M. Using the generic derivative, one defines the tensor fields of torsion and curvature and computes them for all linear derivatives in terms of the quantities $Q_k^{\left(i\right)}\left(X\right)$. The general model is applied to the cases of Lie derivative, covariant derivative, and Fermi derivative. It is shown that the Lie derivative has non-zero torsion and zero curvature due to the Jacobi identity. For the covariant derivative, the standard results follow without any further calculations. Concerning the Fermi derivative, this is defined in a new way, i.e., as a higher-order derivative defined in terms of two derivatives: a given derivative and the Lie derivative. Being linear derivative, it has torsion and curvature tensor. These fields are computed in a general affine space from the corresponding general expressions of the generic derivative. Applications of the above considerations are discussed in a number of cases. Concerning the Lie derivative, it is been shown that the Poisson bracket is in fact a Lie derivative. Concerning the Fermi derivative, two applications are considered: (a) the explicit computation of the Fermi derivative in a general affine space and (b) the consideration of Freedman–Robertson–Walker spacetime endowed with a scalar torsion field, which satisfies the Cosmological Principle and the computation of Fermi derivative of the spatial directions defining a spatial frame along the cosmological fluid of comoving observers. It is found that torsion, even in this highly symmetric case, induces a kinematic rotation of the space axes, questioning the interpretation of torsion as a spin. Finally it is shown that the Lie derivative of the dynamical equations of an autonomous conservative dynamical system is equivalent to the standard Lie symmetry method. Full article

In the covariant averaging scheme of macroscopic gravity, the process of averaging breaks the metricity of geometry. We reinterpret the back-reaction within macroscopic gravity in terms of the non-metricity of averaged geometry. This interpretation extends the effect of back-reaction beyond mere dynamics to the kinematics of geodesic bundles. With a 1 + 3 decomposition of the spacetime, we analyse how geometric flows are modified by deriving the Raychaudhuri and Sachs equations. We also present the modified forms of Gauss and Codazzi equations. Finally, we derive an expression for the angular diameter distance in the Friedmann Lemaître Robertson Walker universe and show that non-metricity modifies it only through the Hubble parameter. Thus, we caution against overestimating the influence of back-reaction on the distances. 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

The existence of ‘peculiar’ velocities due to the formation of cosmic structure marks a point of discord between the real universe and the usually assumed Friedmann–Lemaítre–Robertson–Walker metric, which accomodates only the smooth Hubble expansion on large scales. In the standard $\Lambda$CDM model framework, Type Ia supernovae data are routinely “corrected” for the peculiar velocities of both the observer and the supernova host galaxies relative to the cosmic rest frame, in order to infer evidence for acceleration of the expansion rate from their Hubble diagram. However, observations indicate a strong, coherent local bulk flow that continues outward without decaying out to a redshift $z\gtrsim 0.1$, contrary to the $\Lambda$CDM expectation. By querying the halo catalogue of the Dark Sky Hubble-volume N-body simulation, we find that an observer placed in an unusual environment like our local universe should see correlations between supernovae in the JLA catalogue that are 2–8 times stronger than seen by a typical or Copernican observer. This accounts for our finding that peculiar velocity corrections have a large impact on the value of the cosmological constant inferred from supernova data. We also demonstrate that local universe-like observers will infer a downward biased value of the clustering parameter $S_8$ from comparing the density and velocity fields. More realistic modelling of the peculiar local universe is thus essential for correctly interpreting cosmological data. Full article

It is known that dimensional constants, such as ℏ, c, G, e, and k, are merely human constructs whose values and units vary depending on the chosen system of measurement. Therefore, the time variations in dimensional constants lack operational significance due to their dependence on these dimensional constants. They are well structured and represent a valid discussion. However, this fact only becomes a meaningful debate within the context of a static or present Universe. As theoretically and observationally well established, the current Universe is undergoing accelerated expansion, wherein dimensional quantities, like the wavelength of light, also experience redshift phenomena elongating over cosmic time. In other words, in an expanding Universe, dimensional quantities of physical parameters vary with cosmic time. From this perspective, there exists the possibility that dimensional constants, such as the speed of light, could vary with the expansion of the Universe. In this review paper, we contemplate under what circumstances the speed of light may change or remain constant over cosmic time and discuss the potential for distinguishing these cases observationally. Full article

The main feature of elliptical space—the topological identification of its antipodal points—could be fundamental for understanding the nature of the cosmological redshift. The physical interpretation of the mathematical (topological) structure of elliptical space is made by using physical connections in the form of Einstein-Rosen bridges (also called “wormholes”). The Schwarzschild metric of these structures embedded into a dynamic (expanding) spacetime corresponds to McVittie’s solution of Einstein’s field equations. The cosmological redshift of spectral lines of remote sources in this metric is a combination of gravitational redshift and the time-dependent scale factor of the Friedmann-Lemaitre-Robertson-Walker metric. I compare calculated distance moduli of type-Ia supernovae, which are commonly regarded as “standard candles” in cosmology, with the observational data published in the catalogue “Pantheon+”. The constraint based on these accurate data gives a much smaller expansion rate of the Universe than is currently assumed by modern cosmology, the major part of the cosmological redshift being gravitational by its nature. The estimated age of the Universe within the discussed model is $1.48·{10}^{12}$ yr, which is more than two orders of magnitude larger than the age assumed by using the standard cosmological model parameters. Full article

We consider an alternative to dark matter as a potential solution to various remaining problems in physics: the addition of stochastic perturbations to spacetime to effectively enforce a minimum length and establish a fundamental uncertainty at minimum length (ML) scale. To explore the symmetry of spacetime to such perturbations both in classical and quantum theories, we develop some new tools of stochastic calculus. We derive the generators of rotations and boosts, along with the connection, for stochastically perturbed, minimum length spacetime (“ML spacetime”). We find the metric, the directional derivative, and the canonical commutator preserved. ML spacetime follows the Lie algebra of the Poincare group, now expressed in terms of the two-point functions of the stochastic fields (per Ito’s lemma). With the fundamental uncertainty at ML scale a symmetry of spacetime, we require the translational invariance of any classical theory in classical spacetime to also include the stochastic spacetime perturbations. As an application of these ideas, we consider galaxy rotation curves for massive bodies to find that—under the Robertson–Walker minimum length theory—rotational velocity becomes constant as the distance to the center of the galaxy becomes very large. The new tools of stochastic calculus also set the stage to explore new frontiers at the quantum level. We consider a massless scalar field to derive the Ward-like identity for ML currents. Full article

The suppression of relic gravitational waves due to their conversion into electromagnetic radiation in a cosmological magnetic field is studied. The coupled system of equations describing gravitational and electromagnetic wave propagation in an arbitrary curved space-time and in external magnetic field is derived. The subsequent elimination of photons from the beam due to their interaction with the primary plasma is taken into account. The resulting system of equations is solved numerically in the Friedman–LeMaitre–Robertson–Walker metric for the upper limit of the intergalactic magnetic field strength of 1 nGs. We conclude that the gravitational wave conversion into photons in the intergalactic magnetic field cannot significantly change the amplitude of the relic gravitational wave and their frequency spectrum. Full article

The exact solution of the Hamiltonian constraint in canonical gravity and the resultant reduction of Einstein’s theory reveal the synergy between gravitation and the intrinsic cosmic clock of our expanding universe. Intrinsic Time Geometrodynamics advocates a paradigm shift from four covariance to just spatial diffeomorphism invariance. Consequently, causal time-ordering and quantum Schrödinger–Heisenberg evolution in cosmic time become meaningful. The natural addition of a Cotton–York term to the physical Hamiltonian changes the initial data problem radically. In the classical context, this is studied with the Lichnerowicz–York equation; quantum mechanically, it lends weight to the origin of the universe as an exact Chern–Simons Hartle–Hawking state, which features Euclidean–Lorentzian instanton tunneling. At the level of expectation values, this quantum state yields a low-entropy hot smooth Robertson–Walker beginning in accord with Penrose’s Weyl Curvature Hypothesis. The Chern–Simons Hartle–Hawking state also manifests transverse traceless quantum metric fluctuations, with, at the lowest approximation, scale-invariant two-point correlations as one of its defining characteristics. Full article

The expectation that the physical expansion of space occurs smoothly may be expressed mathematically as a requirement for continuity in the time derivative of the metric scale factor of the Friedmann–Robertson–Walker cosmology. We explore the consequences of imposing such a smoothness requirement, examining the forms of possible interpolating functions between the end of inflation and subsequent radiation- or matter-dominated eras, using a straightforward geometric model of the interpolating behavior. We quantify the magnitude of the cusp found in a direct transition from the end of slow-roll inflation to the subsequent era, analyze the validity of several smooth interpolator candidates, and investigate equation-of-state and thermodynamic constraints. We find an order-of-magnitude increase in the size of the universe at the end of the transition to a single-component radiation or matter era. We also evaluate the interpolating functions in terms of the standard theory of preheating and determine the effect on the number of bosons produced. Full article