Search Results (78)

We investigate the modifications to inflationary observables that arise when adopting an $\alpha$-vacuum instead of the standard Bunch–Davies vacuum for quantum fluctuations during inflation. Within the Starobinsky inflationary model, we compute and compare the scalar spectral index, its running, and the running of the running arising from different choices of the initial vacuum state. We further examine the energy scales associated with $\alpha$-vacua and argue that, for any number of extra spatial dimensions, the relevant scale can be truncated at the Hubble scale, ∼$\mathcal{O}\left({10}^{13}\right)\mathrm{GeV}$, without conflict with current Cavendish-type experimental bounds on sub-millimeter gravity (∼$250\mathsf{\mu }\mathrm{m}$). Our analysis demonstrates that the $\alpha$-vacuum is subject to stringent constraints as a viable de Sitter-invariant alternative to the Euclidean (Bunch–Davies) vacuum, with the corrections that it induces in the inflationary observables being strongly limited by the latest Planck data. Full article

The microscopic origin of the de Sitter entropy remains a central puzzle in quantum gravity that is related to the cosmological constant problem. Within the paradigm of $\mathcal{H}$olographic $\mathcal{N}$aturalness, we propose that this entropy is carried by a vast number of light, coherent degrees of freedom—called “hairons”—which emerge as the moduli of gravitational instantons on orbifolds. Starting from the Euclidean de Sitter instanton ($S^4$), we construct a new class of orbifold gravitational instantons, $S^4/{\mathbb{Z}}_N$, where N corresponds to the de Sitter entropy. We demonstrate that the dimension of the moduli space of these instantons scales linearly with N, and we identify these moduli with the hairon fields. A ${\mathbb{Z}}_N$ symmetry, derived from Wilson loops in the instanton background, ensures the distinguishability of these modes, leading to the correct entropy count. The hairons acquire a mass of the order of the Hubble scale and exhibit negligible mutual interactions, suggesting that the de Sitter vacuum is a coherent state, or Bose–Einstein condensate, of these fundamental excitations. Then, we present a novel framework which unifies neutrino mass generation with the cosmological constant through gravitational topology and holography. The small neutrino mass scale emerges naturally from first principles, without requiring new physics beyond the Standard Model and Gravity. The gravitational Chern–Simons structure and its anomaly with neutrinos force a topological Higgs mechanism, leading to neutrino condensation via $S^4/{\mathbb{Z}}_N$ gravitational instantons. The number of topological degrees of freedom $N\sim M_{\mathrm{P}}^2/\mathrm{\Lambda }\sim {10}^{120}$ provides both the holographic counting of the de Sitter entropy and a $1/N$information see-saw mechanism for neutrino masses. Our framework makes the following predictions: (i) a neutrino superfluid condensation forming Cooper pairs below meV energies, as a viable candidate for cold dark matter; (ii) a possible resolution of the strong CP problem through a QCD composite axion state; (iii) time-varying neutrino masses which track the evolution of dark energy; and (iv) several distinctive signatures in astroparticle physics, ultra-high-energy cosmic rays and high magnetic field experiments. Full article

This work explores late-time gravitational collapse using timelike thin-shell methods in classical general relativity. A junction surface separates a regular de Sitter interior from a Schwarzschild or Schwarzschild–de Sitter exterior in a post-transient regime with fixed exterior mass M (ADM for ${\mathrm{\Lambda }}_{+}=0$), modelling a vacuum–energy core surrounded by an asymptotically classical spacetime. The configuration admits a natural thermodynamic interpretation based on a geometric area functional $S_{\mathrm{shell}}\propto R^2$ and Tolman redshift, both derived from classical junction conditions and used as an entropy-like coarse-grained quantity rather than a fundamental statistical entropy. Key results include (i) identification of a deceleration mechanism at the balance radius $R_{\mathrm{thr}}={(3M/{\mathrm{\Lambda }}_{-})}^{1/3}$ for linear surface equations of state $p=w\sigma$; (ii) classification of the allowable radial domain $V\left(R\right)\le 0$ for outward evolution; (iii) bounded curvature invariants throughout the shell-supported spacetime region; and (iv) a mass-scaled frequency bound $f_c{R}_S\le \xi /\left(3\sqrt{3}\pi \right)$ for persistent near-shell spectral modes. All predictions follow from standard Israel junction techniques and provide concrete observational tests. The framework offers an analytically tractable example of regular thin-shell collapse dynamics within classical general relativity, with implications for alternative compact object scenarios. Full article

The cosmological constant (CC, $\Lambda$) problem stands as one of the most profound puzzles in the theory of gravity, representing a remarkable discrepancy of about 120 orders of magnitude between the observed value of dark energy and its natural expectation from quantum field theory. This paper synthesizes two innovative paradigms—holographic naturalness (HN) and pre-geometric gravity (PGG)—to propose a unified and natural resolution to the problem. The HN framework posits that the stability of the CC is not a matter of radiative corrections but rather of quantum information and entropy. The large entropy $S_{\mathrm{dS}}\sim M_{\mathrm{P}}^2/\Lambda$ of the de Sitter (dS) vacuum (with $M_{\mathrm{P}}$ being the Planck mass) acts as an entropic barrier, exponentially suppressing any quantum transitions that would otherwise destabilize the vacuum. This explains why the universe remains in a state with high entropy and relatively low CC. We then embed this principle within a pre-geometric theory of gravity, where the spacetime geometry and the Einstein–Hilbert action are not fundamental, but emerge dynamically from the spontaneous symmetry breaking of a larger gauge group, SO($1,4$)→SO($1,3$), driven by a Higgs-like field ${\varphi }^A$. In this mechanism, both $M_{\mathrm{P}}$ and $\Lambda$ are generated from more fundamental parameters. Crucially, we establish a direct correspondence between the vacuum expectation value (VEV) v of the pre-geometric Higgs field and the de Sitter entropy: $S_{\mathrm{dS}}\sim v$ (or $v^3$). Thus, the field responsible for generating spacetime itself also encodes its information content. The smallness of $\Lambda$ is therefore a direct consequence of the largeness of the entropy $S_{\mathrm{dS}}$, which is itself a manifestation of a large Higgs VEV v. The CC is stable for the same reason a large-entropy state is stable: the decay of such state is exponentially suppressed. Our study shows that new semi-classical quantum gravity effects dynamically generate particles we call “hairons”, whose mass is tied to the CC. These particles interact with Standard Model matter and can form a cold condensate. The instability of the dS space, driven by the time evolution of a quantum condensate, points at a dynamical origin for dark energy. This paper provides a comprehensive framework where the emergence of geometry, the hierarchy of scales and the quantum-information structure of spacetime are inextricably linked, thereby providing a novel and compelling path toward solving the CC problem. Full article

This study investigates three distinct charged gravastar models within the framework of $f\left(T\right)$ modified gravity, considering the functional forms $f\left(T\right)=T$, $f\left(T\right)=a+bT$, and $f\left(T\right)=T^2$. Inspired by the Mazur–Mottola conjecture, we propose these models as singularity-free alternatives to black holes, each characterized by a three-region structure: (i) an interior de Sitter core, (ii) an intermediate thin shell composed of ultrarelativistic matter, and (iii) an exterior region described by the Reisner Nordstrom solution and other novel spherically symmetric vacuum solutions. We derive a complete set of exact, singularity-free solutions for the charged gravastar configuration, demonstrating their mathematical consistency and physical viability in the context of alternative gravity theories. Notably, the field equations governing the thin shell are solved using an innovative approach based on Killing vector symmetries, eliminating the need for approximations commonly employed in prior studies. Furthermore, we analyze key physical properties of the thin shell, including its proper length, entropy distribution, and energy content. A thorough examination of the energy conditions reveals the thermodynamic stability and viability of these models. Our results contribute to the growing body of work on exotic compact objects and provide new insights into the interplay between modified gravity, electromagnetism, and non-singular black hole alternatives. Full article

In this work, we study field theoretic systems of a single axion-like field with linear potentials modulated by cosine terms, allegedly induced by non-perturbative instanton configurations. These systems are considered in expanding-Universe spacetime backgrounds (of Friedmann–Lema$\widehat{\mathrm{i}}$tre–Robertson–Walker-type). Using a dynamical system approach, we classify the various de Sitter-like (inflationary) vacua from the point of view of their stability, which depend on the values of the model parameters. In this respect, bifurcation points are found to be present for the various models under consideration. Part of the parameter space of the systems under consideration includes the running-vacuum (approximately) linear axion monodromy potentials, considered in previous works by some of the authors, where inflation is induced by primordial gravitational wave condensates. A particularly interesting case, corresponding to another part of the parameter space of the models, includes a series of stable de Sitter vacua, which physically may correspond to a series of successive tunnelings of the system, via say non-perturbative effects, with a decreasing effective cosmological constant. Under certain values of the parameters, these successive tunnelings can reach a Minkowski spacetime, with zero value of the minimum of the axion potential. The situation is not dissimilar to the one of discrete inflation that arguably characterizes some minimal non-critical-string (Liouville) models of cosmology. Finally, for comparison, we also include in this article a dynamical system study of standard axion monodromy-modulated potentials characterizing some string/brane compactification models of inflation. Full article

In this work, we employ the Darmois–Israel thin-shell formalism to construct both static and dynamic thin-shell configurations surrounding traversable wormholes. Initially, using the cut-and-paste technique, we perform a linearized stability analysis in the presence of a general cosmological constant. Our results show that for sufficiently large positive values of the cosmological constant—corresponding to the Schwarzschild–de Sitter geometry—the stability regions of the wormhole solutions are significantly enhanced compared to the Schwarzschild case. Subsequently, we construct static thin-shell solutions by matching an interior wormhole geometry to an exterior vacuum spacetime across a junction surface. In the spirit of minimizing the presence of exotic matter, we identify parameter domains in which the null and weak energy conditions are satisfied at the shell. We examine the surface stress-energy components in detail, determining regions where the tangential surface pressure is either positive or negative, interpreted, respectively, as the pressure or surface tension. Additionally, an expression describing the behavior of the radial pressure across the junction is derived. Finally, we determine key geometrical characteristics of the wormhole, including the throat radius and the junction interface radius, by imposing traversability conditions. Estimates for the traversal time and required velocity are also provided, further elucidating the physical viability of these configurations. Full article

It has been shown that at the present stage of the evolution of the universe, cosmological acceleration is an inevitable kinematical consequence of quantum theory in semiclassical approximation. Quantum theory does not involve such classical concepts as Minkowski or de Sitter spaces. In classical theory, when choosing Minkowski space, a vacuum catastrophe occurs, while when choosing de Sitter space, the value of the cosmological constant can be arbitrary. On the contrary, in quantum theory, there is no uncertainties in view of the following: (1) the de Sitter algebra is the most general ten-dimensional Lie algebra; (2) the Poincare algebra is a special degenerate case of the de Sitter algebra in the limit $R\to \infty$ where R is the contraction parameter for the transition from the de Sitter to the Poincare algebra and R has nothing to do with the radius of de Sitter space; (3) R is fundamental to the same extent as c and ℏ: c is the contraction parameter for the transition from the Poincare to the Galilean algebra and ℏ is the contraction parameter for the transition from quantum to classical theory; (4) as a consequence, the question (why the quantities (c, ℏ, R) have the values which they actually have) does not arise. The solution to the problem of cosmological acceleration follows on from the results of irreducible representations of the de Sitter algebra. This solution is free of uncertainties and does not involve dark energy, quintessence, and other exotic mechanisms, the physical meaning of which is a mystery. Full article

Cutting out an infinite tube around $r=0$ formally removes the Schwarzschild singularity, but without a physical mechanism, this procedure seems ad hoc and artificial. In this paper, we provide justification for such a mechanism by means of non-locality. Motivated by the Gauss law, we define a suitable radius variable as the inverse of a regular non-local potential, and use this variable to model a non-singular black hole. The resulting geometry has a de Sitter core, and for generic values of the regulator, there is no inner horizon, saving this model from potential issues via mass inflation. An outer horizon only exists for masses above a critical threshold, thereby reproducing the conjectured “mass gap” for black holes in non-local theories. The geometry’s density and pressure terms decrease exponentially, thereby rendering it an almost-exact vacuum solution of the Einstein equations outside of astrophysical black holes. Its thermodynamic properties resemble those of the Hayward black hole, with the notable exception that for critical mass, the horizon radius is zero. Full article

We study the Stueckelberg field in de Sitter space, which is a massive vector field with the gauge fixing (GF) term ${\displaystyle \frac{1}{2\zeta }}{({A^{\mu }}_{;\mu })}^2$. We obtain the vacuum stress tensor, which consists of the transverse, longitudinal, temporal, and GF parts, and each contains various UV divergences. By the minimal subtraction rule, we regularize each part of the stress tensor to its pertinent adiabatic order. The transverse stress tensor is regularized to the 0th adiabatic order, while the longitudinal, temporal, and GF stress tensors are regularized to the 2nd adiabatic order. The resulting total regularized vacuum stress tensor is convergent and maximally symmetric, has a positive energy density, and respects the covariant conservation, and thus, it can be identified as the cosmological constant that drives the de Sitter inflation. Under the Lorenz condition ${A^{\mu }}_{;\mu }=0$, the regularized Stueckelberg stress tensor reduces to the regularized Proca stress tensor that contains only the transverse and longitudinal modes. In the massless limit, the regularized Stueckelberg stress tensor becomes zero, and is the same as that of the Maxwell field with the GF term, and no trace anomaly exists. If the order of adiabatic regularization were lower than our prescription, some divergences would remain. If the order were higher, say, under the conventional 4th-order regularization, more terms than necessary would be subtracted off, leading to an unphysical negative energy density and the trace anomaly simultaneously. Full article

In this work, we obtained exact solutions of Einstein’s field equations for plane symmetric cosmological models by assuming that they admit conformal motion. The space-time geometry of these solutions is found to be nonsingular, non-vacuum and conformally flat. We have shown that in the case of a perfect fluid, these solutions have an energy-momentum tensor possessing dark energy with negative pressure and the energy equation of state is $\rho +p=0$. We have shown that a fluid has acceleration, rotation, shear-free, vanishing expansion, and rotation. In the case of a cosmic string cloud, we found that the tension density and particle density decrease as the fluid moves along the direction of the strings, then vanish at infinity. We shown that the exact conformal solution for a static plane symmetric model reduces to the well-known anti-De Sitter space-time. We obtained that the space-time under consideration admits a conformal vector field orthogonal to the 4-velocity vector and does not admits a vector parallel to the 4-velocity vector. Some physical and kinematic properties of the resulting models are also discussed. Full article

In this paper, we investigate the vacuum bosonic current density induced by a carrying-magnetic-flux cosmic string in a $(D+1)$-de Sitter spacetime considering the presence of two flat boundaries perpendicular to it. In this setup, the Robin boundary conditions are imposed on the scalar charged quantum field on the boundaries. The particular cases of Dirichlet and Neumann boundary conditions are studied separately. Due to the coupling of the quantum scalar field with the classical gauge field, corresponding to a magnetic flux running along the string’s core, a nonzero vacuum expectation value for the current density operator along the azimuthal direction is induced. The two boundaries divide the space in three regions with different properties of the vacuum states. In this way, our main objective is to calculate the induced currents in these three regions. In order to develop this analysis we calculate, for both regions, the positive frequency Wightman functions. Because the vacuum bosonic current in dS space has been investigated before, in this paper we consider only the contributions induced by the boundaries. We show that for each region the azimuthal current densities are odd functions of the magnetic flux along the string. To probe the correctness of our results, we take the particular cases and analyze some asymptotic limits of the parameters of the model. Also some graphs are presented exhibiting the behavior of the current with relevant physical parameter of the system. Full article

We investigate the implications of different quantization approaches in Loop Quantum Cosmology for the primordial power spectrum of tensor modes. Specifically, we consider the hybrid and dressed metric approaches to derive the effective mass that governs the evolution of the tensor modes. Our study comprehensively examines the two resulting effective masses and how to estimate them in order to obtain approximated analytic solutions to the tensor perturbation equations. Since Loop Quantum Cosmology incorporates preinflationary effects in the dynamics of the perturbations, we do not have at our disposal a standard choice of privileged vacuum, like the Bunch–Davies state in quasi-de Sitter inflation. We then select the vacuum state by a recently proposed criterion which removes unwanted oscillations in the power spectrum and guarantees an asymptotic diagonalization of the Hamiltonian in the ultraviolet. This vacuum is usually called the NO-AHD (from the initials of Non-Oscillating with Asymptotic Hamiltonian Diagonalization) vacuum. Consequently, we compute the power spectrum by using our analytic approximations and by introducing a suitable numerical procedure, adopting in both cases an NO-AHD vacuum. With this information, we compare the different spectra obtained from the hybrid and the dressed metric approaches, as well as from the analytic and numerical procedures. In particular, this proves the remarkable accuracy of our approximations. 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

A new formalism is introduced that makes it possible to elucidate the physical and geometric content of quantum space–time. It is based on the Minimum Group Representation Principle (MGRP). Within this framework, new results for entanglement and geometrical/topological phases are found and implemented in cosmological and black hole space–times. Our main results here are as follows: (i) We find the Berry phases for inflation and for the cosmological perturbations and express them in terms of the observables, such as the spectral scalar and tensor indices, $n_S$ and $n_T$, and the tensor-to-scalar ratio r. The Berry phase for de Sitter inflation is imaginary with the sign describing the exponential acceleration. (ii) The pure entangled states in the minimum group (metaplectic) $Mp\left(n\right)$ representation for quantum de Sitter space–time and black holes are found. (iii) For entanglement, the relation between the Schmidt type representation and the physical states of the $Mp\left(n\right)$ group is found: This is a new non-diagonal coherent state representation complementary to the known Sudarshan diagonal one. (iv) Mean value generators of $Mp\left(2\right)$ are related to the adiabatic invariant and topological charge of the space–time, (matrix element of the transition $-\infty <t<\infty$). (v) The basic even and odd n-sectors of the Hilbert space are intrinsic to the quantum space–time and its discrete levels (in particular, continuum for $n\to \infty$), they do not require any extrinsic generation process such as the standard Schrodinger cat states, and are entangled. (vi) The gravity or cosmological domains on one side and another of the Planck scale are entangled. Examples: The quantum primordial trans-Planckian de Sitter vacuum and the classical late de Sitter vacuum today; the central quantum gravity region and the external classical gravity region of black holes. The classical and quantum dual gravity regions of the space–time are entangled. (vii) The general classical-quantum gravity duality is associated with the Metaplectic $Mp\left(n\right)$ group symmetry which provides the complete full covering of the phase space and of the quantum space–time mapped from it. Full article