Search Results (58)

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, I investigate gravitational thermodynamics of the Einstein–Maxwell–scalar system in three dimensions without a cosmological constant. In a previous work by Krishnan, Shekhar, and Bala Subramanian, it was argued that this system has no BH saddles, but has only empty (flat space) saddles and boson star saddles. It was then concluded that the structure of the thermodynamic phase space is much simpler than in the higher-dimensional cases. I will show that, in addition to the known boson star and empty saddles, three more types of saddles exist in this system: the BG saddle, its hairy generalization, and a novel configuration called the boson star-PL saddle. As a result, the structure is richer than one might naively expect and is very similar to the higher-dimensional ones. Full article

It has been shown that if one solves self-consistently the semiclassical Einstein equations in the presence of a quantum scalar field, with a cutoff on the number of modes, spacetime become flatter when the cutoff increases. Here, we extend the result to include the effect of fields with spin 0, 1/2, 1 and 2. With minor adjustments, the main result persists. Remarkably, one can have positive curvature even if the cosmological constant in the bare action is negative. Full article

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 non-minimal coupling and includes, in addition to the Riemann tensor, Ricci tensor, and Ricci scalar, as well as 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, which 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 that appear 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 the early Universe due to the non-minimal interaction with the spacetime curvature. Full article

In this paper, we introduce and conduct a comprehensive study of pseudo-Schouten symmetric manifolds ${\left(PSS\right)}_n$. We establish necessary and sufficient conditions for such a manifold to be Einstein and quasi-Einstein, respectively. Next, we examine pseudo-Schouten symmetric spacetimes within the framework of general relativity. Furthermore, we investigate their role in relativistic spacetime models by considering Einstein’s field equations with and without a cosmological constant. We also show that pseudo-Schouten symmetric spacetimes satisfying Einstein’s equations with a quadratic Killing energy–momentum tensor or a Codazzi-type energy–momentum tensor cannot have non-zero constant scalar curvature. Finally, the existence of pseudo-Schouten symmetric spacetime is shown by constructing an explicit non-trivial example. Full article

Making use of the well-known renormalization group (RG) scale dependences of the gravitational couplings in the framework of the two-parameter Einstein–Hilbert (EH) theory of gravity, the single scalar field-driven cosmological inflation is discussed in a spatially homogeneous, isotropic, and flat model universe. The inflaton field is represented by a one-component real, non-self-interacting, massive scalar field minimally coupled to gravity. Cases without and with the incorporation of the RG scaling of the inflaton mass are compared with each other and with the corresponding classical case. It is shown that the quantum improvement drastically alters the timing of the slow-roll inflation with the desirable number $\underset{,}{\mathrm{N}}\approx 60$ e-foldings, as compared with the classical case. Furthermore, accounting for the RG flow of the inflaton mass has an enormous effect on the timing of the desirable slow roll, too. Although providing the desirable slow-roll inflation, none of the versions of the investigated quantum-improved toy models provide a realistic value of the amplitude of the scalar perturbations. 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

In the initial part of this paper, we survey (in arbitrary spacetime dimension) the general FLRW cosmologies with non-interacting perfect fluids and with a canonical or phantom scalar field, minimally coupled to gravity and possibly self-interacting; after integrating the evolution equations for the fluids, any model of this kind can be described as a Lagrangian system with two degrees of freedom, where the Lagrange equations determine the evolution of the scale factor and the scalar field as functions of the cosmic time. We analyze specific solvable models, paying special attention to cases with a phantom scalar; the latter favors the emergence of nonsingular cosmologies in which the Big Bang is replaced, e.g., with a Big Bounce or a periodic behavior. As a first example, we consider the case with dust (i.e., pressureless matter), radiation, and a scalar field with a constant self-interaction potential (this is equivalent to a model with dust, radiation, a free scalar field and a cosmological constant in the Einstein equations). In the phantom subcase (say, with nonpositive spatial curvature), this yields a Big Bounce cosmology, which is a non-absurd alternative to the standard ($\Lambda$CDM) Big Bang cosmology; this Big Bounce model is analyzed in detail, even from a quantitative viewpoint. We subsequently consider a class of cosmological models with dust and a phantom scalar, whose self-potential has a special trigonometric form. The Lagrange equations for these models are decoupled passing to suitable coordinates $(x,y)$, which can be interpreted geometrically as Cartesian coordinates in a Euclidean plane: in this description, the scale factor is a power of the radius $r=\sqrt{x^2+y^2}$. Each one of the coordinates $x,y$ evolves like a harmonic repulsor, a harmonic oscillator, or a free particle (depending on the signs of certain constants in the self-interaction potential of the phantom scalar). In particular, in the case of two harmonic oscillators, the curves in the plane described by the point $(x,y)$ as a function of time are the Lissajous curves, well known in other settings but not so popular in cosmology. A general comparison is performed between the contents of the present work and the previous literature on FLRW cosmological models with scalar fields, to the best of our knowledge. Full article

Our paper introduces a new theoretical framework called the Fractional Einstein–Gauss–Bonnet scalar field cosmology, which has important physical implications. Using fractional calculus to modify the gravitational action integral, we derived a modified Friedmann equation and a modified Klein–Gordon equation. Our research reveals non-trivial solutions associated with exponential potential, exponential couplings to the Gauss–Bonnet term, and a logarithmic scalar field, which are dependent on two cosmological parameters, m and ${\alpha }_0=t_0{H}_0$ and the fractional derivative order $\mu$. By employing linear stability theory, we reveal the phase space structure and analyze the dynamic effects of the Gauss–Bonnet couplings. The scaling behavior at some equilibrium points reveals that the geometric corrections in the coupling to the Gauss–Bonnet scalar can mimic the behavior of the dark sector in modified gravity. Using data from cosmic chronometers, type Ia supernovae, supermassive Black Hole Shadows, and strong gravitational lensing, we estimated the values of m and ${\alpha }_0$, indicating that the solution is consistent with an accelerated expansion at late times with the values ${\alpha }_0=1.38\pm 0.05$, $m=1.44\pm 0.05$, and $\mu =1.48\pm 0.17$ (consistent with ${\mathrm{\Omega }}_{m,0}=0.311\pm 0.016$ and $h=0.712\pm 0.007$), resulting in an age of the Universe $t_0=19.0\pm 0.7$ [Gyr] at 1$\sigma$ CL. Ultimately, we obtained late-time accelerating power-law solutions supported by the most recent cosmological data, and we proposed an alternative explanation for the origin of cosmic acceleration other than $\mathrm{\Lambda }$CDM. Our results generalize and significantly improve previous achievements in the literature, highlighting the practical implications of fractional calculus in cosmology. Full article

The entire classical cosmological history between two extreme de Sitter vacuum solutions is discussed based on Einstein’s equations and non-equilibrium thermodynamics. The initial non-singular de Sitter state is characterised by a very high energy scale, which is equal or smaller than the reduced Planck mass. It is structurally unstable, and all of the continuous created matter, energy, and entropy of the material component comes from the irreversible flow powered by the primeval vacuum energy density. The analytical expression describing the running vacuum is obtained from the thermal approach. It opens a new perspective to solve the old puzzles and current observational challenges plaguing the cosmic concordance model driven by a rigid vacuum. Such a scenario is also modelled through a non-canonical scalar field. It is demonstrated that the resulting scalar field model is shown to be a step-by-step a faithful analytical representation of the thermal running vacuum cosmology. Full article

Since the development of Brans–Dicke gravity, it has become well-known that a conformal transformation of the metric can reformulate this theory, transferring the coupling of the scalar field from the Ricci scalar to the matter sector. Specifically, in this new frame, known as the Einstein frame, Brans–Dicke gravity is reformulated as General Relativity supplemented by an additional scalar field. In 1959, Hans Adolf Buchdahl utilized an elegant technique to derive a set of solutions for the vacuum field equations within this gravitational framework. In this paper, we extend Buchdahl’s method to incorporate the cosmological constant and to the scalar-tensor cases beyond the Brans–Dicke archetypal theory, thereby, with a conformal transformation of the metric, obtaining solutions for a version of Brans–Dicke theory that includes a quadratic potential. More specifically, we obtain synchronous solutions in the following contexts: in scalar-tensor gravity with massless scalar fields, Brans–Dicke theory with a quadratic potential, where we obtain specific synchronous metrics to the Schwarzschild–de Sitter metric, the Nariai solution, and a hyperbolically foliated solution. Full article

We investigate a spherically symmetric exact solution of Einstein’s gravity with cosmological constant in (2 + 1) dimensions, non-minimally coupled to a scalar field. The solution describes the gravitational field of a black hole, which is free of curvature singularities in the entire spacetime. We use the formalism of geometrothermodynamics to investigate the geometric properties of the corresponding space of equilibrium states and find their interpretation from the point of view of thermodynamics. It turns out that, as a result of the presence of thermodynamic interaction, the space of equilibrium states is curved with two possible configurations, which depend on the value of a coupling constant. In the first case, the equilibrium space is completely regular, corresponding to a stable thermodynamic system. The second case is characterized by the presence of two curvature singularities, which are shown to correspond to locations where the system undergoes two different phase transitions, one due to the breakdown of the thermodynamic stability condition and the second one due to the presence of a divergence at the level of the response functions. 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

This paper reviews the dynamics of a single isotropic and homogeneous scalar field $\phi \left(t\right)$ in the context of cosmological models. A non-standard approach to the solution of the Einstein–Klein–Gordon equations is described which uses the scalar field as the evolution parameter for cosmic dynamics. General conclusions about the qualitative behaviour of the solutions can be drawn, and examples of how to obtain explicit solutions for some cosmological models of interest are given. For arbitrary potentials, analytical results can be obtained from the slow-roll approximation by using a series expansion for the Hubble parameter $H\left[\phi \right]$, from which a quantitative estimate for the number of e-folds of expansion is obtained. This approach is illustrated with the examples of quadratic potentials and hilltop models, with special consideration of Higgs-type potentials. The GUT-scale is shown to come out of such a model quite naturally. Finally, it is discussed how to find scalar potentials giving rise to a predetermined scalar-field behaviour and the associated evolution of the scale factor. Full article

Fractional differential calculus is a mathematical tool that has found applications in the study of social and physical behaviors considered “anomalous”. It is often used when traditional integer derivatives models fail to represent cases where the power law is observed accurately. Fractional calculus must reflect non-local, frequency- and history-dependent properties of power-law phenomena. This tool has various important applications, such as fractional mass conservation, electrochemical analysis, groundwater flow problems, and fractional spatiotemporal diffusion equations. It can also be used in cosmology to explain late-time cosmic acceleration without the need for dark energy. We review some models using fractional differential equations. We look at the Einstein–Hilbert action, which is based on a fractional derivative action, and add a scalar field, $\varphi$, to create a non-minimal interaction theory with the coupling, $\xi R{\varphi }^2$, between gravity and the scalar field, where $\xi$ is the interaction constant. By employing various mathematical approaches, we can offer precise schemes to find analytical and numerical approximations of the solutions. Moreover, we comprehensively study the modified cosmological equations and analyze the solution space using the theory of dynamical systems and asymptotic expansion methods. This enables us to provide a qualitative description of cosmologies with a scalar field based on fractional calculus formalism. Full article