Search Results (28)

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

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

In a seminal work, Hawking showed that natural states for free quantum matter fields on classical spacetimes that solve the spherically symmetric vacuum Einstein equations are KMS states of non-vanishing temperature. Although Hawking’s calculation does not include the backreaction of matter on geometry, it is more than plausible that the corresponding Hawking radiation leads to black hole evaporation which is, in principle, observable. Obviously, an improvement of Hawking’s calculation including backreaction is a problem of quantum gravity. Since no commonly accepted quantum field theory of general relativity is available yet, it has been difficult to reliably derive the backreaction effect. An obvious approach is to use the black hole perturbation theory of a Schwarzschild black hole of fixed mass and to quantize those perturbations. However, it is not clear how to reconcile perturbation theory with gauge invariance beyond linear perturbations. In recent work, we proposed a new approach to this problem that applies when the physical situation has an approximate symmetry, such as homogeneity (cosmology), spherical symmetry (Schwarzschild), or axial symmetry (Kerr). The idea, which is surprisingly feasible, is to first construct the non-perturbative physical (reduced) Hamiltonian of the reduced phase space of fully gauge invariant observables and only then apply perturbation theory directly in terms of observables. The task to construct observables is then disentangled from perturbation theory, thus allowing to unambiguously develop perturbation theory to arbitrary orders. In this first paper of the series we outline and showcase this approach for spherical symmetry and second order in the perturbations for Einstein–Klein–Gordon–Maxwell theory. Details and generalizations to other matter and symmetry and higher orders will appear in subsequent companion papers. Full article

It has been proven that in standard Einstein gravity, exotic matter (i.e., matter violating the pointwise and averaged Weak and Null Energy Conditions) is required to stabilize traversable wormholes. Quantum field theory permits these violations due to the quantum coherent effects found in any quantum field. Even reasonable classical scalar fields violate the energy conditions. In the case of the Casimir effect and squeezed vacuum states, these violations have been experimentally proven. It is advantageous to investigate methods to minimize the use of exotic matter. One such area of interest is extended theories of Einstein gravity. It has been claimed that in some extended theories, stable traversable wormholes solutions can be found without the use of exotic matter. There are many extended theories of gravity, and in this review paper, we first explore $f\left(R\right)$ theories and then explore some wormhole solutions in $f\left(R\right)$ theories, including Lovelock gravity and Einstein Dilaton Gauss–Bonnet (EdGB) gravity. For completeness, we have also reviewed ‘Other wormholes’ such as Casimir wormholes, dark matter halo wormholes, thin-shell wormholes, and Nonlocal Gravity (NLG) wormholes, where alternative techniques are used to either avoid or reduce the amount of exotic matter that is required. Full article

The detection of gravitational waves in 2015 ushered in a new era of gravitational wave (GW) astronomy capable of probing the strong field dynamics of black holes and neutron stars. It has opened up an exciting new window for laboratory and space tests of Einstein’s theory of classical general relativity (GR). In recent years, two interesting proposals have aimed to reveal the quantum nature of perturbative gravity: (1) theoretical predictions on how graviton noise from the early universe, after the vacuum of the gravitational field was strongly squeezed by inflationary expansion; (2) experimental proposals using the quantum entanglement between two masses, each in a superposition (gravitational cat, or gravcat) state. The first proposal focuses on the stochastic properties of quantum fields (QFs), and the second invokes a key concept of quantum information (QI). An equally basic and interesting idea is to ask whether (and how) gravity might be responsible for a quantum system becoming classical in appearance, known as gravitational decoherence. Decoherence due to gravity is of special interest because gravity is universal, meaning, gravitational interaction is present for all massive objects. This is an important issue in macroscopic quantum phenomena (MQP), underlining many proposals in alternative quantum theories (AQTs). To fully appreciate or conduct research in these exciting developments requires a working knowledge of classical GR, QF theory, and QI, plus some familiarity with stochastic processes (SPs), namely, noise in quantum fields and decohering environments. Traditionally a new researcher may be conversant in one or two of these four subjects: GR, QFT, QI, and SP, depending on his/her background. This tutorial attempts to provide the necessary connective tissues between them, helping an engaged reader from any one of these four subjects to leapfrog to the frontier of these interdisciplinary research topics. In the present version, we shall address the three topics listed in the title, excluding gravitational entanglement, because, despite the high attention some recent experimental proposals have received, its nature and implications in relation to quantum gravity still contain many controversial elements. Full article

Unimodular gravity is one of the oldest geometric gravity theories and alternatives to general relativity. Essentially, it is based on the Einstein–Hilbert Lagrangian with an additional constraint on the determinant of the metric. It can be explicitly shown that unimodular gravity can be recast as general relativity in the presence of a cosmological constant. This fact has led to many discussions on the equivalence of both theories at the classical and quantum levels. Here, we present an analysis focused on the classical scalar perturbations around a cosmological background. We focus on the unusual situation in which the typical conservation laws are not adopted. The discussion is extended to the case where a non-minimal coupled scalar field is introduced. We also present a gauge-invariant analysis showing that perturbations in unimodular gravity display instabilities. Our results reinforce that the equivalence is not verified completely at a cosmological perturbative level. Full article

This paper deals with the problem of establishing a systematic theoretical formulation of variational principles for the continuum gravitational field dynamics of classical General Relativity (GR). In this reference, the existence of multiple Lagrangian functions underlying the Einstein field equations (EFE) but having different physical connotations is pointed out. Given validity of the Principle of Manifest Covariance (PMC), a set of corresponding variational principles can be constructed. These are classified in two categories, respectively, referred to as constrained and unconstrained Lagrangian principles. They differ for the normalization properties required to be satisfied by the variational fields with respect to the analogous conditions holding for the extremal fields. However, it is proved that only the unconstrained framework correctly reproduces EFE as extremal equations. Remarkably, the synchronous variational principle recently discovered belongs to this category. Instead, the constrained class can reproduce the Hilbert–Einstein formulation, although its validity demands unavoidably violation of PMC. In view of the mathematical structure of GR based on tensor representation and its conceptual meaning, it is therefore concluded that the unconstrained variational setting should be regarded as the natural and more fundamental framework for the establishment of the variational theory of EFE and the consequent formulation of consistent Hamiltonian and quantum gravity theories. Full article

The cosmological constant and its phenomenology remain among the greatest puzzles in theoretical physics. We review how modifications of Einstein’s general relativity could alleviate the different problems associated with it that result from the interplay of classical gravity and quantum field theory. We introduce a modern and concise language to describe the problems associated with its phenomenology, and inspect no-go theorems and their loopholes to motivate the approaches discussed here. Constrained gravity approaches exploit minimal departures from general relativity; massive gravity introduces mass to the graviton; Horndeski theories lead to the breaking of translational invariance of the vacuum; and models with extra dimensions change the symmetries of the vacuum. We also review screening mechanisms that have to be present in some of these theories if they aim to recover the success of general relativity on small scales as well. Finally, we summarize the statuses of these models in their attempts to solve the different cosmological constant problems while being able to account for current astrophysical and cosmological observations. Full article

Background independence is often being claimed as the characteristic property of several current and past models of Quantum Gravity. In actual fact, such a notion has a wider connotation and must be rooted into the validity of the general covariance principle, demanding its logical connection with the notions of manifest covariance and (quantum) gauge invariance. In fact, as we intend to show here, it involves (a) the existence of a well-defined, albeit arbitrary, classical background space-time; and (b) the suitable realization of a dynamical equation for the related background metric field tensor, referred to as quantum-modified Einstein tensor field equation, which actually determines it in a suitable functional setting. Remarkably, it is proved that in the context of the theory of Covariant Quantum Gravity (CQG-theory), recently developed by Cremaschini and Tessarotto (2015–2022), background independence implies that such an equation “emerges” rigorously from the same CQG-theory. This follows in terms of a stochastic quantum expectation value evaluated with respect to the corresponding characteristic quantum PDE. It is shown that an analogous emergence property applies also to the background metric field tensor in terms of stochastic fluctuations of the corresponding underlying quantum tensor of gravitational field. These results warrant the consistent validity of background independence for the prescription of the space-time metric tensor in CQG-theory. Full article

The present work deals with two kinds of k-essence dark energy models within the framework of loop quantum cosmology (LQC). The two kinds of k-essence models originates from two forms of Lagrangians, i.e., ${\mathcal{L}}_1=F\left(X\right)V(\varphi )$ and ${\mathcal{L}}_2=F\left(X\right)-V(\varphi )$, where $F\left(X\right)$ and $V(\varphi )$ stand for the kinetic term and potential of the scalar field $\varphi$, respectively. Two models are based on different phase variables settings, and the general form of autonomous dynamical system is deduced for each Lagrangian. Then, the dynamical stabilities of the critical points in each model are analysed in different forms of $F\left(X\right)$ and $V(\varphi )$. Model I is a 3-dim system with four stable points, and Model II is a 4-dim system but reduced to a 3-dim system using the symmetry analysis, which has five stable points. Moreover, the corresponding cosmological quantities, such as ${\Omega }_{\varphi }$, $w_{\varphi }$ and q, are calculated at each critical point. To compare these with the case of the classical Einstein cosmology (EC), the dynamical evolutionary trajectories in the phase space and evolutionary curves of the cosmological quantities are drawn for both EC and LQC cases, which shows that the loop quantum gravity effects diminish in the late-time universe but are significant in the early time. Further, the effects of interaction $Q=\alpha H{\rho }_m$ on the evolutions of the universe are discussed. With the loop quantum gravity effects, bouncing universe is achieved in both models for different initial values of ${\varphi }_0$, ${\dot{\varphi }}_0$, $H_0$, ${\rho }_0$ and coupling parameter $\alpha$, which helps to avoid singularities. However, the interaction has little effect on bounce, although it is important to the stability of some critical points. Full article

The “ER = EPR” conjecture, conceived by Maldacena and Susskind, is grounded on the notion that a gravitational theory in the bulk is dual to the corresponding quantum field theory on the boundary in accordance to the AdS/CFT correspondence. The conjecture pertains to the idea that Einstein-Rosen (ER) spacetime bridges and Einstein-Podolsky-Rosen (EPR) quantum entanglement may be considered as dually equivalent. Since ER bridges refer to the connectivity between black holes, the “ER = EPR” conjecture implies that black holes connected by ER bridges are entangled, and conversely, that entangled black holes are connected by ER bridges. However, the instance of the maximally entangled tripartite (GHZ) quantum state points to the necessity of devising a model of non-classical Planck scale ER bridges going beyond the standard description of these bridges in spacetime. Based on the topological structure of the maximally entangled GHZ state, we propose that a universal topological link, called the Borromean rings, furnishes a particular linking structure that is able to unravel the equavalence between entanglement and wormholes, and thus, to address the validity of the “ER = EPR” conjecture beyond the initial context of the AdS/CFT correspondence. As a consequence, we propose the explicit construction of distinguishable extensions of the smooth classical spacetime manifold taking place in the transition to the quantum gravity regime according to a naturally induced physical criterion of gravitational generic properties following from this intrinsic topological qualification of the “ER = EPR” conjecture. Full article

In this paper, the effects of the quantum metric fluctuations on the background cosmological dynamics of the universe are considered. To describe the quantum effects, the metric is assumed to be given by the sum of a classical component and a fluctuating component of quantum origin . At the classical level, the Einstein gravitational field equations are equivalent to a modified gravity theory, containing a non-minimal coupling between matter and geometry. The gravitational dynamics is determined by the expectation value of the fluctuating quantum correction term, which can be expressed in terms of an arbitrary tensor $K_{\mu \nu }$. To fix the functional form of the fluctuation tensor, the Newtonian limit of the theory is considered, from which the generalized Poisson equation is derived. The compatibility of the Newtonian limit with the Solar System tests allows us to fix the form of $K_{\mu \nu }$. Using these observationally consistent forms of $K_{\mu \nu }$, the generalized Friedmann equations are obtained in the presence of quantum fluctuations of the metric for the case of a flat homogeneous and isotropic geometry. The corresponding cosmological models are analyzed using both analytical and numerical method. One finds that a large variety of cosmological models can be formulated. Depending on the numerical values of the model parameters, both accelerating and decelerating behaviors can be obtained. The obtained results are compared with the standard $\Lambda$CDM ($\Lambda$ Cold Dark Matter) model. Full article

The logarithmic correction to Bekenshtein–Hawking entropy in the framework of 4D Einstein–Gauss–Bonnet gravity coupled with nonlinear electrodynamics is obtained. We explore the black hole solution with the spherically symmetric metric. The logarithmic term in the entropy has a structure similar to the entropy correction in the semi-classical Einstein equations. The energy emission rate of black holes and energy conditions are studied. The quasinormal modes of a test scalar field are investigated. The gravitational lensing of light around BHs was studied. We calculated the deflection angle for some model parameters. Full article

A new type of quantum correction to the structure of classical black holes is investigated. This concerns the physics of event horizons induced by the occurrence of stochastic quantum gravitational fields. The theoretical framework is provided by the theory of manifestly covariant quantum gravity and the related prediction of an exclusively quantum-produced stochastic cosmological constant. The specific example case of the Schwarzschild–deSitter geometry is looked at, analyzing the consequent stochastic modifications of the Einstein field equations. It is proved that, in such a setting, the black hole event horizon no longer identifies a classical (i.e., deterministic) two-dimensional surface. On the contrary, it acquires a quantum stochastic character, giving rise to a frame-dependent transition region of radial width $\delta r$ between internal and external subdomains. It is found that: (a) the radial size of the stochastic region depends parametrically on the central mass M of the black hole, scaling as $\delta r\sim M^3$; (b) for supermassive black holes $\delta r$ is typically orders of magnitude larger than the Planck length $l_P$. Instead, for typical stellar-mass black holes, $\delta r$ may drop well below $l_P$. The outcome provides new insight into the quantum properties of black holes, with implications for the physics of quantum tunneling phenomena expected to arise across stochastic event horizons. Full article

Gravity formulated as a classical gauge theory is based on the Mach principle in terms of curvature scalar R by A. Einstein. The original idea of Einstein limits the gravity to act as a curvature in spacetime. However, there exist other possible classical fields such as torsion and non-metricity. The aim of this paper is to make a compatible comparison between three paradigms: Gravity as curvature via Einstein–Hilbert action, Teleparallel Gravity (TEGR) and Coincidence Gravity (CGR). In TEGR, a flat spacetime is considered as well as an asymmetric connection metric. In CGR, gravity is constructed in an equally flat, tortionless spacetime, which is ascribed to non-metricity. The strength and weakness of each formulation is tested in the framework of a homogeneous and isotropic cosmological background. Mainly, the equivalence between GR and TEGR is examined at the level of equation of motion. Furthermore, we study the interactions between dark energy, dark matter and radiation, and the stability of these models is explored. The implications of the interaction were tested in both early and late epochs of the universe. It has been found that mostly there is a similarity of description of the evolution of the universe provided by GR and TEGR, while CGR always showed different description. Full article