We clarify the role of the Null Energy Condition (NEC) in the context of the current cosmological data. In particular, the NEC implies the sum of the total energy density and pressure satisfies ρ tot + P tot ≥ 0; the energy conditions do not apply separately to individual components of the cosmological fluid. Consequently, we show that under the current best-fit w 0-wa cosmological model no violation of the NEC takes place, in the past or extrapolated to the future. Further, growth in the energy density of an individual component cannot be used to signal violation of the NEC. We illustrate these points with a worked example whereby misestimation of the matter density leads to a phase during which ρde + Pde < 0 for the effective dark energy, followed by a phantom crossing and subsequent ρde + Pde > 0. At no time is the NEC violated.

Abstract We present a systematic construction of traversable wormhole spacetimes featuring two symmetric throats within the framework of General Relativity. Our approach employs the embedding formalism by imposing the analytic relation $$r - r_0 = K(z^2 - a)^2$$ r - r 0 = K ( z 2 - a ) 2 between the radial coordinate and the embedding function, which naturally guarantees the flare-out condition at both throats. This ansatz yields a composite shape function b ( r ) consisting of two branches: an asymptotically flat branch ( $$\epsilon = +1$$ ϵ = + 1 ) extending to spatial infinity, and an intermediate tunnel branch ( $$\epsilon = -1$$ ϵ = - 1 ) with restricted domain $$r_0 \le r \le r_0 + Ka^2$$ r 0 ≤ r ≤ r 0 + K a 2 , connecting the two throats positioned at $$z = \pm \sqrt{a}$$ z = ± a with separation $$2\sqrt{a}$$ 2 a . Analysis of the Einstein field equations reveals that the supporting matter violates the weak, null, and dominant energy conditions throughout the spacetime, while the strong energy condition is identically satisfied with $$\rho + p_r + 2p_t = 0$$ ρ + p r + 2 p t = 0 . A critical finding is the direct connection between throat separation and energy density: configurations with $$0&lt; a &lt; 1/(16Kr_0)$$ 0 &lt; a &lt; 1 / ( 16 K r 0 ) admit positive energy density at the throats with phantom-type radial pressure ( $$\omega _r &lt; -1$$ ω r &lt; - 1 ) and dark-energy-like effective behavior ( $$\omega _{\text {eff}} &lt; 0$$ ω eff &lt; 0 ), whereas larger separations $$a &gt; 1/(16Kr_0)$$ a &gt; 1 / ( 16 K r 0 ) require negative energy density. Notably, configurations with phantom matter at the throats require such small values of a that the intermediate tunnel region becomes almost imperceptible, with the two throats nearly coincident, approaching the limiting case of a single-throat geometry. The geometric structure is visualized through embedding diagrams, which demonstrate that increasing the parameter a produces more pronounced and sharply defined throats. This work establishes that multi-throat wormhole geometries can be systematically generated through embedding techniques, providing a complementary approach to field-theoretic constructions and revealing how topological complexity relates to exotic matter distributions in traversable spacetimes.

The inflationary paradigm has transformed our understanding of the early universe; yet most inflationary models are considered geodesically past-incomplete, suggesting a beginning of time or a primordial Big Bang singularity. The Borde–Guth–Vilenkin (BGV) theorem is often cited as demonstrating that all eternally inflating spacetimes must be past-incomplete. Utilizing a new theorem establishing geodesic completeness in generalized cosmologies, we present a simple, explicit class of inflationary solutions that are smooth, nonsingular, and geodesically complete for all time, including into the past. These models exhibit localized NEC violation but remain globally well-behaved in both temporal directions. The NEC violation is confined and controlled: the averaged null energy condition (ANEC) is satisfied in the strongest sense, while violations of smeared null energy conditions (SNEC) are uniformly bounded and become nonnegative under sufficiently wide smearings. Our results suggest that eternal inflation can arise from controlled NEC-violating dynamics, offering a new, nonsingular, and past-eternal picture of the universe.

The main objective of this work is to explore the theoretical existence of traversable wormholes in Rastall teleparallel theory under the matter source described by solitonic quantum wave and Navarro-Frenk-White density profiles. We utilize the Morris-Thorne geometric setup to describe the wormhole geometry, from which the anisotropic field equations are obtained in terms of the torsion scalar. Under a constant redshift function, we derive the shape functions in connection with both dark matter models and examine their compliance with traversability conditions. Both the obtained functions satisfy the defined criteria, creating a topological bridge between asymptotically flat spacetimes. The existence of wormhole solutions is further investigated by measuring the extent to which they violate the null energy condition. We further investigate other geometric features, such as computation of the active gravitational mass, the volume integral quantifier, the embedding diagrams, and an evaluation of the anisotropy. The analysis confirms that both wormhole solutions are theoretically viable under the presence of exotic fluid within the considered teleparallel-based framework.

In this study, we explore the late-time cosmic acceleration using the [Formula: see text] gravity framework, where the non-metricity Q is coupled to the matter Lagrangian [Formula: see text]. We investigate a nonlinear model defined by [Formula: see text]. To reconstruct the cosmological evolution, we employ a kinematic ansatz with a logarithmic parametrization of the deceleration parameter, [Formula: see text]. We constrain the model parameters using the latest observational data from Cosmic Chronometers (CC) and Baryon Acoustic Oscillations (BAO) via the Dark Energy Spectroscopic Instrument (DESI). The Markov Chain Monte Carlo (MCMC) analysis yields a current Hubble parameter of [Formula: see text] and indicates a transition from deceleration to acceleration at [Formula: see text]. Solving the modified Friedmann equations allows us to determine the evolution of the Hubble parameter and effective thermodynamic quantities. Further, we analyze the energy density ([Formula: see text]), pressure (p), and Equation of State (EoS) parameter ([Formula: see text]). Additionally, we distinguish the proposed [Formula: see text] model from the standard [Formula: see text]CDM paradigm using geometrical diagnostics, including the Statefinder hierarchy [Formula: see text] and [Formula: see text], as well as cosmographic parameters like Jerk, lerk and Snap. Finally, we test the model’s validity against standard Energy Conditions. The results demonstrate that while the model violates the Strong Energy Condition (SEC) to support cosmic acceleration, it satisfies the Null Energy Condition (NEC) within the observational range, ensuring the stability of the cosmic fluid.

We establish a general no-go theorem demonstrating that all traversable wormhole configurations in Unimodular Gravity necessarily require exotic matter. The proof relies solely on the geometric flaring-out condition, b′(r0) ≤ 1, which directly implies that ρ(r0) + pr(r0) ≤ 0 at the throat. This condition represents a violation of the Null Energy Condition and, consequently, of the Weak and Strong Energy Conditions, independently of the particular choice of shape function, redshift function, or equation of state. This result holds for both tidal and zero-tidal-force configurations, showing that the requirement of exotic matter is a fundamental geometric consequence of the traversability condition rather than an artifact of specific solution choices. Therefore, Unimodular Gravity shares this fundamental constraint with General Relativity.

Abstract In this work, we investigate exact black string solutions in the context of f ( R , T ) gravity. Adopting the specific form $$f(R,T) = R + 2\chi T$$ f ( R , T ) = R + 2 χ T , we consider an anisotropic Kiselev fluid as the matter content and obtain static cylindrical solutions, which are then extended to the rotating case through a suitable coordinate transformation. The influence of the quintessence state parameter $$w_q$$ w q and the matter–geometry coupling constant $$\chi $$ χ on the geometry is analyzed. We examine the weak, null, and strong energy conditions, identifying the regions in the parameter space where they are satisfied. Furthermore, we apply the Hamilton–Jacobi method to study the tunneling of scalar particles across the event horizon and derive the corresponding Hawking temperature. The thermodynamic stability of the solutions is investigated by computing the heat capacity, and the conditions for phase transitions are discussed. The results provide a characterization of black strings in f ( R , T ) gravity surrounded by quintessence, highlighting the combined effects of anisotropic matter and modified gravity on their physical properties.

Abstract We construct a class of wormhole geometries supported by the non-local gravitational self-energy that regularizes the particle and black-hole sectors of spacetime. Using this framework, inspired by T-duality, we show that two entangled particles (or particle–black-hole pairs) naturally source an Einstein-Rosen–type geometry in which the required violation of the strong energy condition arises from intrinsic quantum-gravity effects rather than from ad hoc exotic matter, which is matter that violates the null energy condition. We classify the resulting wormholes, analyze their horizons, throat structure and embedding properties, and we identify the exotic energy needed at the minimal surface. Imposing the $$\textrm{ER}=\textrm{EPR}$$ ER = EPR requirement of non-traversability and the absence of a macroscopic throat, we find that only the zero-throat geometry is compatible with an entanglement-induced Einstein–Rosen bridge, providing a concrete realization of $$\textrm{ER}=\textrm{EPR}$$ ER = EPR within a fully regular spacetime. Finally, we briefly discuss possible implications for microscopic ER networks from vacuum fluctuations, replica-wormhole interpretations of Hawking radiation, and possible links to entanglement-driven dark-energy scenarios.

This study investigates the impact of bulk viscosity on the viability of cosmic bounce solutions in the framework of [Formula: see text] gravity, where non-metricity is defined by Q and matter-Lagrangian density is represented by [Formula: see text]. For this purpose, we study the behavior of a flat Friedmann–Robertson–Walker universe model with isotropic matter configuration and new formulation of the bulk viscosity coefficient as [Formula: see text]. Here, [Formula: see text] and n are positive constants and [Formula: see text] represents the bounce epoch. We analyze the influence of this modified framework on the evolution of the universe by considering a specific functional form of this modified theory. We examine several cosmological parameters to analyze the evolution of the universe. Our outcomes indicate that the pressure is negative, energy density is positive and the presence of a singularity-free bounce in this gravitational model is ensured by the violation of null energy condition. The state parameter suggests behavior consistent with a quintessence regime or a phantom era. We conclude that it provides effective substitutes for the standard paradigms of cosmology, hence this yields important perspectives into the early universe and the nature of force of gravitation.

A bstract Scalar fields in theories of gravity often inhabit a moduli space of vacua, and coherent spatial or temporal variations in their expectation values can produce measurable gravitational effects. Such variations are expected in contexts ranging from inflationary cosmology to the near-horizon regions of near-extremal black holes, where they can deflect light rays and shift horizons. This work derives a quantitative field excursion bound (FEB) on scalar variations along null geodesics, expressed in terms of the expansion parameter. The bound follows from the Raychaudhuri equation, assuming that all other fields satisfy the null energy condition (NEC). It is saturated in certain spacetimes containing a timelike naked singularity. A possible generalization to semiclassical spacetimes that violate the NEC, but satisfy a strengthened version of the quantum focusing condition (QFC), is proposed. In cosmology, the FEB constrains the extent of large field excursions to be linearly bounded by the number of e-folds, independent of the inflationary model. This has notable implications for anthropic scenarios, where large excursions are often invoked to access favorable vacua.

Abstract In this draft, we investigate constant redshift function Morris–Thorne-like traversable wormhole (WH) models which described as a relativistic static fluid distribution in Schwarzschild-type coordinates with a topological global monopole charge under the influence of D -dimensional Einstein gravity. In this scenario we consider three distinct shape functions, while matter sector is supported by anisotropic fluid configuration. We show some basic criteria for the viability of all three shape function models, the radial null energy condition is generally violated while tangential components are satisfied in the vicinity of the throat for appropriately chosen parameter values. We examine that the active gravitational mass becomes negative near the throat which indicates the existence of exotic matter (EM) and positive anisotropy parameter helps in maintaining the throat stability, while the adiabatic indices lie above the relativistic threshold supporting the stability of the WH configurations. We also employ the complexity factor as a diagnostic tool for anisotropy and density inhomogeneity which reveals that the WH geometries evolve toward minimal complexity at large radial distances. We analyze the influence of monopole parameter on the WH’s throat and curvature through 2 D and 3 D embedding diagrams, however, the total amount of EM is estimated by utilizing volume integral quantifier (VIQ) approach in our considered gravity theory.

Within the framework of asymptotically safe gravity, we investigate traversable wormhole configurations sourced by dark matter halos modeled through the Burkert density profile. In this setting, the wormhole shape function is determined by the interplay between the adopted mass-density distribution and the modified gravitational field equations. The analysis proceeds by employing the tangential velocity profile to infer the redshift function. A scale-dependent gravitational coupling, G ( k ) , obtained from the infrared renormalization group flow of asymptotically safe gravity, is incorporated into the field equations to consistently include quantum gravitational corrections at astrophysical length scales. We analyze the standard energy conditions and demonstrate that the null energy condition is violated in the neighborhood of the wormhole throat, in agreement with the generic behavior of traversable wormhole spacetimes. Furthermore, we construct embedding diagrams to visualize the spatial geometry and to elucidate the flaring–out condition at the throat.

ABSTRACT We construct 4D de Sitter space as an excited state, rather than as a vacuum configuration, in type IIB, heterotic , and heterotic string theories. This framework provides a mechanism to evade vacuum‐based no‐go theorems for de Sitter solutions in string theory. Starting from a generic M‐theory configuration, we obtain de Sitter isometry in the dual string theories through appropriate dynamical duality sequences in the late‐time limit. The excited state, identified as a Glauber–Sudarshan state, is constructed as the expectation value of the metric operator in M‐theory using path‐integral techniques. We further analyze the conditions required for the existence of a well‐defined effective field theory description and show that these conditions are equivalent to the null energy condition for a 4D Friedmann‐Lemaitre‐Robertson‐Walker cosmology. Finally, we investigate constraints arising from axionic cosmology, and demonstrate how the time‐dependent solutions are modified when experimental bounds on the axionic coupling constant are taken into account. This article serves as a computational companion to Sections 3 and 4 of the paper arXiv:2511.03798 [hep‐th], where we present the detailed intermediate steps underlying the analysis in those sections.

The violation of the null energy condition (NEC) is essential for constructing nonsingular cosmological scenarios, such as Genesis cosmology, which avoids the initial singularity by initiating cosmic evolution from an asymptotically Minkowski state. To address theoretical concerns regarding the accumulation of negative energy, the smeared null energy condition (SNEC) has been proposed as a quantum-motivated, semi-local bound on NEC violation. In this work, we examine the implications of the SNEC conjecture for Genesis models, typically constructed within generalized Galileon theories. Our results demonstrate that SNEC imposes nontrivial restrictions on the viability of Genesis models, highlighting the SNEC conjecture as a powerful tool for constraining nonsingular cosmological scenarios.

Abstract In this paper, we construct and analyze a new class of static, spherically symmetric wormhole geometries supported by anisotropic matter distributions inspired by the Einasto density profile, which is widely used to describe dark matter haloes in galaxies. We discuss the geometrical and physical implications of such wormhole configurations through a variable redshift function in the context of general relativity. Within this model, a number of physical constraints are taken into consideration, including energy conditions (like the null energy condition) and the conservation equation, which bring critical checks on the viability of traversable configurations. We further discuss the EoS parameter, the behavior of the anisotropy factor, and the exoticity parameter, all of which, taken together, determine the matter content supporting the wormhole throat. In this respect, we present the active gravitational mass function along with the embedding diagram in order to better visualize the geometrical properties of the considered wormhole. For completeness, we then consider the Kretschmann scalar, which characterizes the geometrical properties and verifies the absence of singularities in the whole domain. We also analyze the complexity factor associated with the matter distribution to give an indication about the internal structure and gravitational behavior of the wormhole. The impact of the Einasto profile on such physical and geometrical quantities is emphasized, showing that dark matter-inspired models for the density can rightfully minimize the amount of exotic matter within this class of traversable wormholes. Indeed, this formally demonstrates that the framework here considered does provide physically acceptable solutions that are asymptotically flat and points towards the fundamental contribution of dark matter distributions in the building-up of stable wormhole geometries.

Abstract In this work, we present an exact solution describing a static, spherically symmetric black hole immersed in a cored Navarro–Frenk–White (NFW) dark matter halo. We examine the energy conditions and find that the null, weak, strong and dominant energy conditions are all satisfied, confirming the physical plausibility of our solution. Furthermore, we examine its optical and scalar perturbation properties, highlighting their connections to the Lyapunov exponent and black hole thermodynamics. By applying the principle of least action, we derive the null geodesics to study gravitational lensing and light ring phenomena in the presence of the dark matter halo. The stability of photon orbits is analyzed using the Lyapunov exponent, which we relate to the imaginary part of the massless quasinormal modes in the eikonal limit. We also investigate the thermodynamic behavior of the black hole–dark matter system by evaluating the mass function, entropy, temperature, heat capacity, Gibbs free energy and the entropy to assess both local and global stability. Overall, our results demonstrate that the surrounding dark matter halo significantly influences the black hole’s properties, enhancing its thermodynamic stability and allowing the possibility of phase transitions.

Abstract We study slowly rotating traversable wormholes embedded in realistic galactic dark matter halos, including Navarro–Frenk–White (NFW), Bose–Einstein Condensate (Thomas-Fermi, TF), and pseudo-isothermal (PI) profiles. Using the Teo-type rotating wormhole metric, we construct shape functions from halo density distributions and analyze the resulting geometrical properties, such as throat structure, flaring-out conditions, and violations of the null energy condition. We examine null geodesics, effective potentials, photon spheres, and Lense-Thirring (LT) precession, highlighting differences between cuspy and cored halo models. Finally, we calculate wormhole shadows, observing that cuspy NFW halos tend to produce smaller, asymmetric shadows, while cored TF and PI halos yield smoother, nearly circular silhouettes. The findings provide a theoretical characterization of photon dynamics and shadow morphology in wormholes embedded within different dark matter environments.

A bstract In holography, the isometry group of the bulk spacetime corresponds to the symmetries of the boundary theory. We thus approach the question of whether (and when) scale invariance in combination with Poincaré invariance implies full conformal invariance in quantum field theory from a holographic bulk perspective. To do so, we study bulk spacetimes that include a warped extra dimension and in which the isometry group corresponds to scale without conformal invariance. Firstly, we show that the bulk Weyl tensor plays a pivotal role in distinguishing those metrics exhibiting conformal invariance (Weyl=0) from those merely exhibiting scale invariance (Weyl≠0). Based on this, we then prove the following theorem: for putative boundary theories with n ≥ 2 dimensions, the bulk metric can not exhibit scale without conformal invariance if its warped extra dimension is compact and the null energy condition is required to hold. For n = 1, we discuss that a more general ansatz for the bulk metric must be made, a detailed analysis of which is left for future research. A 12-minute video abstract can be found at https://youtu.be/J_jHazxEvVk .

We analyze the physical properties of an analytical, nonsingular quantum-corrected black hole solution recently derived in a minisuperspace model for unimodular gravity under the assumption of unitarity in unimodular time. We show that the metric corrections compared to the classical Schwarzschild solutions only depend on a single new parameter, corresponding to a minimal radius where a black hole-white hole transition occurs. While these corrections substantially alter the structure of the spacetime near this minimal radius, they fall off rapidly toward infinity, and we show in various examples how physical properties of the exterior spacetime are very close to those of the Schwarzschild solution. We derive the maximal analytic extension of the initial solution, which corresponds to an infinite sequence of Kruskal spacetimes connected via black-to-white hole transitions, and compare with some other proposals for nonsingular black hole metrics. The metric violates the achronal averaged null energy condition, which indicates that we are capturing physics beyond the semiclassical approximation. Finally, we include some thoughts on how to go beyond the simple eternal black hole-white hole model presented here.

Abstract This paper studies the impact of bulk viscosity on the feasibility of the cosmological bounce solutions in the framework of F ( R ) theory. In this perspective, the behavior of an isotropic homogeneous universe with a perfect matter configuration and new formulation of the bulk viscosity coefficient is explored. We select a specific mathematical form of the modified gravity model to see how it affects the dynamics of cosmic evolution. In addition, we analyze various cosmological parameters, exploring the presence of feasible cosmological bounce solutions. A physically acceptable bouncing scenario occurs when the energy density stays positive, pressure becomes negative, and the violation of null and strong energy conditions highlight the important role of bulk viscosity. We also study the cosmographic parameters and their paths in the $$r-s$$ r - s diagnostic framework. Finally, a thermodynamic investigation is carried out to test the generalized second law of thermodynamics and the overall stability of the cosmological model. The results show that F ( R ) gravity is a realistic and promising alternative to the standard cosmological model, giving deeper understanding of gravitational dynamics and the early evolution of cosmos.