Search Results (19)

We carry out a careful analysis of the notion of observation of distant events in a curved Universe. This leads us to hypothesise that all measurements of our physical environment are performed with respect to a representation referential that obeys the rules of Euclidean geometry. In curved spacetime geometries, this creates a distortion of metric quantities which affects the wavelength of photons incoming from distant sources. We show that, at the scale of our galaxy, this effect is too small to be experimentally detected. At a cosmological scale, however, and in the context of the Einstein Universe, we show that it becomes measurable and offers a simple alternative explanation for most modern cosmological observations. In particular, we predict a redshift which increases as a function of the source’s distance, in a way that is consistent with Supernovae data, and the existence of a Cosmic Microwave Background whose characteristics align with the ones measured by the Planck mission. Furthermore, it accounts for the presence of well-formed galactic structures in the high-redshift Universe, as recently detected by the James Webb Space Telescope. 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

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

Einstein–Cartan theory is a generalization of general relativity that introduces spacetime torsion. In this paper, we perform phase space analysis to investigate the evolution of the early universe in Einstein–Cartan theory. By studying the stability of critical points in the dynamical system, we find that there exist two stable critical points which represent an Einstein static solution and an expanding solution, respectively. After analyzing the phase diagram of the dynamical system, we find that the early universe may exhibit an Einstein static state, an oscillating state, or a bouncing state. By assuming the equation of state $\omega$ can decrease over time t, the universe can depart from the initial Einstein static state, oscillating state, or bouncing state and then evolve into an inflationary phase. Then, we analyze four different inflationary evolution cases in Einstein–Cartan theory and find that a time-variable equation of state $\omega$ cannot yield values of $n_s$ and r consistent with observations, while a time-invariant equation of state $\omega$ is supported by the Planck 2018 results. Thus, in Einstein–Cartan theory, the universe likely originates from a bouncing state rather than an Einstein static state or an oscillating state. Full article

Alternative scenarios where the Big Bang singularity of the standard cosmological model is replaced by a bounce, or by an early almost static phase (known as emergent universe) have been frequently studied. We investigate the role of the spinor degrees of freedom in overcoming the initial singularity. We introduce a model which generalizes the Einstein–Cartan–Dirac theory, including local phase invariance of the spinor field supported by a gauge scalar field and certain couplings to the torsion. A natural gauge choice reduces the field equations to that of the Einstein–Dirac theory with a Dirac field potential that has polar and axial spinor currents. We identify a new potential term proportional to the square of the ratio of Dirac scalar and axial scalar, which provides a dark energy contribution dominating in the late-time Universe. In addition, the presence of spinor currents in the potential may induce the bounce of a contracting universe. Full article

The spin-torsion theory is a gauge theory approach to gravity that expands upon Einstein’s general relativity (GR) by incorporating the spin of microparticles. In this study, we further develop the spin-torsion theory to examine spherically symmetric and static gravitational systems that involve free-falling macroscopic particles. We posit that the quantum spin of macroscopic matter becomes noteworthy at cosmic scales. We further assume that the Dirac spinor and Dirac equation adequately capture all essential physical characteristics of the particles and their associated processes. A crucial aspect of our approach involves substituting the constant mass in the Dirac equation with a scale function, allowing us to establish a connection between quantum effects and the scale of gravitational systems. This mechanism ensures that the quantum effect of macroscopic matter is scale-dependent and diminishes locally, a phenomenon not observed in microparticles. For any given matter density distribution, our theory predicts an additional quantum term, the quantum potential energy (QPE), within the mass expression. The QPE induces time dilation and distance contraction, and thus mimics a gravitational well. When applied to cosmology, our theory yields a static cosmological model. The QPE serves as a counterpart to the cosmological constant introduced by Einstein to balance gravity in his static cosmological model. The QPE also offers a plausible explanation for the origin of Hubble redshift (traditionally attributed to the universe’s expansion). The predicted luminosity distance–redshift relation aligns remarkably well with SNe Ia data from the cosmological sample of SNe Ia. In the context of galaxies, the QPE functions as the equivalent of dark matter. The predicted circular velocities align well with rotation curve data from the SPARC (Spitzer Photometry and Accurate Rotation Curves database) sample. Importantly, our conclusions in this paper are reached through a conventional approach, with the sole assumption of the quantum effects of macroscopic matter at large scales, without the need for additional modifications or assumptions. Full article

The Janis–Newman–Winicour spacetime corresponds to a static spherically symmetric solution of Einstein equations with the energy momentum tensor of a massless quintessence field. It is understood that the spacetime describes a naked singularity. The solution has two parameters, b and s. To our knowledge, the exact physical meaning of the two parameters is still unclear. In this paper, starting from the Janis–Newman–Winicour naked singularity solution, we first obtain a wormhole solution by a complex transformation. Then, letting the parameter s approach infinity, we obtain the well-known exponential wormhole solution. After that, we embed both the Janis–Newman–Winicour naked singularity and its wormhole counterpart in the background of a de Sitter or anti-de Sitter universe with the energy momentum tensor of massive quintessence and massive phantom fields, respectively. To our surprise, the resulting quintessence potential is actually the dilaton potential found by one of us. It indicates that, by modulating the parameters in the charged dilaton black hole solutions, we can obtain the Janis–Newman–Winicour solution. Furthermore, a charged wormhole solution is obtained by performing a complex transformation on the charged dilaton black hole solutions in the background of a de Sitter or anti-de Sitter universe. We eventually find that s is actually related to the coupling constant of the dilaton field to the Maxwell field and b is related to a negative mass for the dilaton black holes. A negative black hole mass is physically forbidden. Therefore, we conclude that the Janis–Newman–Winicour naked singularity solution is not physically allowed. Full article

The emergent universe provides a possible method to avoid the Big Bang singularity by considering that the universe stems from a stable Einstein static universe rather than the singularity. Since the Einstein static universe exists before inflation, it may leave some relics in the CMB power spectrum. In this paper, we analyze the stability condition for the Einstein static universe in general relativity with k-essence against both the scalar and tensor perturbations. Furthermore, we find the emergent universe can be successfully realized by constructing a scalar potential and an equation of state parameter. Solving the curved Mukhanov–Sasaki equation, we obtain the analytical approximation for the primordial power spectrum, and then depict the TT-spectrum of the emergent universe. The results show that both the primordial power spectrum and CMB TT-spectrum are suppressed on large scales. Full article

The main objective of this article is to examine the stability of Einstein static universe using inhomogeneous perturbations in the context of energy–momentum squared gravity. For this purpose, we used FRW spacetime with perfect matter distribution and formulated static as well as perturbed field equations. We took a minimal model of this theory to investigate the stable regions of the Einstein universe for conserved and non-conserved energy–momentum tensors. We found that stable modes of the Einstein universe appeared in both conserved and non-conserved cases for all values of the equation of state and model parameters corresponding to both open and closed cosmic models. We found that stable solutions in this modified theory were obtained for a broader $\omega$-region compared to other modified theories. Full article

The de Sitter spacetime is a maximally symmetric spacetime. It is one of the vacuum solutions to Einstein equations with a cosmological constant. It is the solution with a positive cosmological constant and describes a universe undergoing accelerated expansion. Among the possible signs for a cosmological constant, this solution is relevant for primordial and late-time cosmology. In the case of a zero cosmological constant, studies on the representations of its isometry group have led to a broader understanding of particle physics. The isometry group of $d+1$-dimensional de Sitter is the group $SO(d+1,1)$, whose representations are well known. Given this insight, what can we learn about the elementary degrees of freedom in a four dimensional de Sitter universe by exploring how the unitary irreducible representations of $SO(4,1)$ present themselves in cosmological setups? This article aims to summarize recent advances along this line that benefit towards a broader understanding of quantum field theory and holography at different signs of the cosmological constant. Particular focus is given to the manifestation of $SO(4,1)$ representations at the late-time boundary of de Sitter. The discussion is concluded by pointing towards future questions at the late-time boundary and the static patch with a focus on the representations. Full article

Spacetime torsion is known to be highly suppressed at the end of inflation, which is called preheating. This result was recently shown in (EPJ C (2022)) in the frame of Einstein–Cartan–Brans–Dicke inflation. In this paper, it is shown that a torsionful magnetogenesis in QED effective Lagrangean drives a torsion damping in order to be subsequently amplified by the dynamo effect after the generation of these magnetic fields seeds. This damping on amplification would depend upon the so-called torsion chirality. Here, a cosmic factor $gkK$ is present where K is the contortion vector and k is the wave vector which is connected to the inverse of magnetic coherence length. In a second example, we find Higgs inlationary fields in Einstein–Cartan gravity thick domain walls (DWs). Recently, a modified Einstein–Cartan gravity was given by Shaposhnikov et al. [PRL (2020)] to obtain Higgs-like inflatons as a portal to dark energy. In the case of thick DW, we assume that there is a torsion squared influence, since we are in the early universe where torsion is not so weak as in the late universe as shown by Paul and SenGupta [EPJ C (2019)] in a 5D brane-world. A static DW solution is obtained when the inflationary potential vanishes and Higgs potential is a helical function. Recently, in the absence of inflation, domain wall dynamos were obtained in Einstein–Cartan gravity (EC) where the spins of the nucleons were orthogonal to the wall. Full article

In this work, the static cosmological model of the Schwarzschild solution for the solar system is proposed taking into account the cosmological constant in the equation of the general theory of relativity (GTR) proposed by A. Einstein. We found the nonlinear differential equation that describes the behavior of the planets around the Sun; this is solved exactly by the Jacobi and Weierstrass elliptic functions. The obtained solution allows for us to estimate the value of the cosmological constant knowing the perihelion of the different planets and from different mathematical approaches; that is, the inverse problem is solved. From the obtained results, the Schwarzschild static cosmological model for the solar system is proposed, establishing the Schwarzschild cosmological radius and the curvature limit of the solar system. From the curvature limit, different regions are proposed for the planets, exoplanets, and a region is predicted where the existence of new planets and exoplanets belonging to the solar system is possible. The proposed theory of the static Schwarzschild cosmological model may be of great interest to astronomers, cosmologists, and all those interested in the study of the universe. Full article

The Einstein cylinder is the first cosmological model for our universe in modern history. Its geometry not only describes a static universe—a universe being invariant under time reversal—but it is also the prototype for a maximally symmetric spacetime with constant positive curvature. As such, it is still of crucial importance in numerous areas of physics and engineering, offering a fruitful playground for simulations and new theories. Here, we focus on the implementation and simulation of acoustic wave propagation on the Einstein cylinder. Engineering such an extraordinary device is the territory of metamaterial science, and we will propose an appropriate tuning of the relevant acoustic parameters in such a way as to mimic the geometric properties of this spacetime in acoustic space. Moreover, for probing such a space, we derive the corresponding wave equation from a variational principle for the underlying curved spacetime manifold and examine some of its solutions. In particular, fully analytical results are obtained for concentric wave propagation. We present predictions for this case and thereby investigate the most significant features of this spacetime. Finally, we produce simulation results for a more sophisticated test model which can only be tackled numerically. Full article

We present a comparative analysis of the self-gravitating solitons that arise in the Einstein–Klein–Gordon, Einstein–Dirac, and Einstein–Proca models, for the particular case of static, spherically symmetric spacetimes. Differently from the previous study by Herdeiro, Pombo and Radu in 2017, the matter fields possess suitable self-interacting terms in the Lagrangians, which allow for the existence of Q-ball-type solutions for these models in the flat spacetime limit. In spite of this important difference, our analysis shows that the high degree of universality that was observed by Herdeiro, Pombo and Radu remains, and various spin-independent common patterns are observed. Full article

We study the Jeans instability of an infinite homogeneous dissipative self-gravitating Bose–Einstein condensate described by generalized Gross–Pitaevskii–Poisson equations [Chavanis, P.H. Eur. Phys. J. Plus2017, 132, 248]. This problem has applications in relation to the formation of dark matter halos in cosmology. We consider the case of a static and an expanding universe. We take into account an arbitrary form of repulsive or attractive self-interaction between the bosons (an attractive self-interaction being particularly relevant for the axion). We consider both gravitational and hydrodynamical (tachyonic) instabilities and determine the maximum growth rate of the instability and the corresponding wave number. We study how they depend on the scattering length of the bosons (or more generally on the squared speed of sound) and on the friction coefficient. Previously obtained results (notably in the dissipationless case) are recovered in particular limits of our study. Full article