We present a new real tachyon vacuum solution in cubic superstring field theory, constructed without square roots or phantom terms. Although gauge equivalence to known non-real solutions might suggest identical physical observables, this correspondence is not guaranteed: even in the bosonic theory, gauge-equivalent solutions can yield divergent or ill-defined results for physical quantities. In the supersymmetric case, the situation is further complicated by the presence of the picture-changing operator in the definition of the action and inner product, which requires careful treatment. Building on the KBcγ algebra, our square-root-free solution avoids potential branch cut ambiguities. By explicitly addressing these subtleties, we rigorously compute the vacuum energy and verify that the equation of motion, when contracted with the solution itself, is satisfied. The results confirm consistency with Sen's conjecture and provide a mathematically consistent foundation for further developments in the construction of analytic, real solutions in superstring field theory.

A bstract In neutrino-dense astrophysical environments, these particles exchange flavor through a coherent weak field, forming a collisionless neutrino plasma with collective flavor dynamics. Instabilities, which grow and affect the environment, may arise from neutrino-neutrino refraction alone (fast limit), vacuum energy splittings caused by masses (slow limit), or neutrino-matter scattering (collisional limit). We present a comprehensive analytical description of the dispersion relation governing these unstable modes. Treating vacuum energy splittings and collision rates as small perturbations, we construct a unified framework for fast, slow, and collisional instabilities. We classify modes into gapped , where collective excitations are already present in the fast limit but rendered unstable by slow or collisional effects, and gapless , which are purely generated by these effects. For each class, we derive approximate dispersion relations for generic energy and angle distributions, which reveal the order of magnitude of the growth rates and the nature of the instabilities without solving directly the dispersion relation. This approach confirms that slow and collisionally unstable waves generally grow much more slowly than they oscillate. Consequently, the common fast-mode approximation of local evolution within small boxes is unjustified. Even for fast modes, neglecting large-distance propagation of growing waves, as usually done, may be a poor approximation. Our unified framework provides an intuitive understanding of the linear phase of flavor evolution across all regimes and paves the way for a quasi-linear treatment of the instability’s nonlinear development.

We seek order in a hard matter by trusting two guides that do not mislead: positivity and invariance. From a reflection-positive lattice formulation of SU(N) Yang-Mills, choosing on each time slice a definite transverse form and gently damping distant modes, we proceed by steps that preserve these guides. From such simple means we pass to the continuum: Euclidean correlation functions satisfy the Osterwalder-Schrader axioms, and the Wightman theory with a unique vacuum and positive energy follows. The decisive point is the scale: time-correlations are completely monotone and decay uniformly, so the spectral measure cannot touch zero; and along the same flow the vacuum-orthogonal evolution decays at a fixed rate, which survives in the limit. Thus a strictly positive, volume-independent spectral gap is obtained for the continuum Hamiltonian, and the bridge from Euclidean positivity to Hilbert-space dynamics remains intact.

The 2012 discovery of the Higgs boson at the Large Hadron Collider (LHC) marked a triumph for the Standard Model (SM) and Quantum Field Theory (QFT), confirming the mechanism for particle mass generation through spontaneous symmetry breaking. However, this paper reinterprets the LHC results within Dynamic Vacuum Field Theory (DVFT), a unified framework where the vacuum is a dynamic complex scalar field ϕ(x)=ρ(x)e^(iθ(x)). In DVFT, the Higgs boson emerges as a radial excitation of the vacuum amplitude ρ, providing a physical substrate that resolves SM/QFT limitations such as the hierarchy problem, vacuum energy discrepancy, and failure to unify gravity. Detailed derivations demonstrate how DVFT reproduces the Higgs-like particle while extending to general relativity and cosmology. Comparisons highlight DVFT's superiority in offering causal explanations without ad hoc parameters, positioning it as a foundational alternative to SM/QFT.

Emergence of running vacuum energy in f(R, T) gravity : Observational constraints

HydroNanoConstruct is a web application with a graphical user interface (GUI) that enables the digital construction and analysis of hydrated metal/metalloid oxide (ΜΟ) nanoparticles (NPs). The tool supports (a) building hydrated ΜΟ NPs from crystallographic information files (CIFs) of MOs by adding hydrogen cations, hydroxyl anions, and water molecules to the surface atoms, preserving the bulk material's coordination numbers for the metal/metalloid atoms, (b) performing energy minimization on the digitally constructed hydrated MO NPs to obtain realistic structures, (c) embedding the hydrated MO NP into a simulation box filled with water molecules to incorporate solvent effects, and (d) running multiple molecular dynamics and energy minimization cycles to compute atomistic descriptors, including surface energy (in vacuum and in water) and the potential energy of the bulk material. The tool is freely available via the EosCloud Platform at https://eoscloud.entelos.eu/ssbd4chem/nanoconstruct/.

A theory for ground-state modifications of matter embedded in a Fabry-Perot cavity and whose excitations are described as harmonic oscillators is presented. Based on Lifshitz's theory for vacuum energy and employing a Lorentz model for the material permittivity, a nonperturbative macroscopic QED model that accounts for the infinite number of cavity modes with a continuum of their wave vectors was built. Differences from the commonly used single-mode Hopfield Hamiltonian are revealed. The nonresonant role of polaritons in the ground-state energy shift is also demonstrated, showing that the cavity effect is mainly caused by static screening occurring at very low frequencies. The theory allows for a straightforward incorporation of losses and temperature effects.

Abstract We develop a unified dynamical systems framework for spatially flat FLRW cosmology in f ( Q ) gravity, covering all three connection branches using a single set of Hubble-normalised variables without fixing the function f ( Q ) a priori. This model-independent and connection-agnostic approach enables direct comparison across connection choices and uncovers structural features of the cosmological dynamics not visible in connection-specific formulations. While the existing works narrowly focus only on fixed point analysis, in our work we put special efforts to identify the invariant submanifolds, model-independent trajectories and physically viable regions of phase space across connections. For a broad class of viable f ( Q ) models, we establish the generic existence of de Sitter attractors and matter-dominated fixed points in the two branches of connection, offering a robust route to late-time acceleration without fine-tuning. We further identify an invariant submanifold that yields $$\Lambda $$ Λ CDM-like background evolution despite underlying dynamics distinct from General Relativity, providing a geometric origin for cosmic acceleration distinguishable only at the perturbation level. We also derive a first integral on this submanifold, allowing analytic reconstruction of the dynamical connection and uncovering hidden conservation laws. Another key feature we found is that while trivial connections exhibit strong parameter dependence, the nontrivial branches often feature parameter-independent behaviours. We also study the variation of the effective gravitational coupling, $$k_{\text {eff}}$$ k eff , across branches and show how this can be constrained using astrophysical observations, which bridges theoretical viability with observational consistency in a novel way. Applying our framework to the illustrative model $$f(Q)=\alpha Q + \beta (-Q)^n$$ f ( Q ) = α Q + β ( - Q ) n , we find late-time acceleration and $$\Lambda $$ Λ CDM-like behaviour without vacuum energy. Finally, we propose a general route for extending dynamical systems analysis to broader classes of f ( Q ) models using the $$m_i$$ m i -hierarchy method. This framework enables closure for models previously inaccessible to standard approaches and offers a diagnostic tool for identifying structurally viable cosmologies within modified gravity theories.

Vacuum energy and topological mass from a constant magnetic field and boundary conditions in coupled scalar field theories

A bstract We calculate the θ dependence in a cousin of QCD, where the vacuum structure can be analyzed exactly. The theory is $$ \mathcal{N} $$ N = 2 SU(2) gauge theory with N F = 0, 1, 2, 3 flavors of fundamentals, explicitly broken to $$ \mathcal{N} $$ N = 1 via an adjoint superpotential, and coupled to anomaly mediated supersymmetry breaking (AMSB). The hierarchy m AMSB ≪ μ 𝒩=1 ≪ Λ ensures the validity of our IR analysis. As expected from ordinary QCD, the vacuum energy is a function of θ which undergoes 1st order phase transitions between different vacua where the various dyons condense. For N F = 0 we find the expected phase transition at θ = π , while for N F = 1, 2, 3 we find phase transitions at fractional values of π .

The standard model of the universe, λ CDM , is based on the Friedmann-Lemaître-Robertson-Walker metric with a flat three-dimensional coordinate space and the Friedmann equations Navas . [.]. The cosmological constant λ provides the cancellation of the matter field contributions in the flat (Minkowski) space, as was proposed long ago in 1967 by Zeldovich for the first time to our knowledge Zeldovich [ , 316 (1967)]; see also Krasinski and Zeldovich []. The dynamical dark energy appears on the surface of the vacuum energy of matter fields at the flat (Minkowski) space. Within the Standard Model, the gluon Yang-Mills (YM) fields are playing a specific role since the properties of their vacuum, where there is the presence of the gluon condensate, provide the nonperturbative vacuum energy. It is natural to apply the successful instanton liquid model of the QCD vacuum and its lowest excitations. Our aim is to calculate the contribution of gluon YM fields to the dark energy density. We find that the universe metric is generating the QCD vacuum excitation, which gives the contribution to the dark energy density. But this one may hardly play a central role in the dynamics of the universe, since its timescale is too small. We also find the equation-of-state parameters w 0 = − 1 , w a = 0 in accordance with λ CDM , while the newest data, analyzed at Shajib and Frieman [.], give them at least in the range − 0.91 < w 0 < − 0.73 , − 1.05 < w a < − 0.65 . They are requesting a contribution from an ultralight scalar such as an axion, or from YM field topological configurations with the nontrivial holonomy due to the deviation from a pure de Sitter state Van Waerbeke and Zhitnitsky [DESI results and dark energy from QCD topological sectors, .].

Interacting model of bulk viscous and decaying vacuum energy

This work proposes a geometric-statistical reinterpretation of the dark sector, grounded in a discrete spacetime framework composed of non-material spatial units termed hodons. Unlike particle-based dark matter models, hodons are kinematically inert and possess ultra-light effective mass derived from vacuum energy density and holographic volume bounds. We introduce a covariant scalar field representing local hodon density and derive an entropy-driven evolution equation consistent with causal structure and general relativity. The resulting stress-energy contribution from hodon fluctuations yields gravitational clumpiness without invoking new particles or modified gravity. A virial-based toy model demonstrates that baryonic matter surrounded by hodons forms stable, cored halo profiles, consistent with galactic rotation curves and low-mass halo observations. The framework naturally suppresses small-scale structure via spatial uncertainty relations, aligning with constraints from the Lyman-α forest and weak lensing. By integrating Bousso's covariant entropy bound and distinguishing between strong and weak holography, we situate the model within a broader epistemological context. These results suggest that dark sector phenomenology may emerge from the statistical geometry of space itself, offering a falsifiable alternative to particle dark matter.

A direct interaction between dark energy and dark matter provides a natural and important extension to the standard ΛCDM cosmology. We perform a non-parametric reconstruction of the vacuum energy (w = -1) interacting with cold dark matter using the cosmological data from DESI DR2, Planck CMB, and three SNIa samples (PP, DESY5, and Union3). By discretizing the coupling function β(z) into 20 redshift bins and assuming a Gaussian smoothness prior, we reconstruct β(z) without assuming any specific parameterization. The mean reconstructed β(z) changes sign during cosmic evolution, indicating an energy transfer from cold dark matter to dark energy at early times and a reverse flow at late times. At high redshifts, β(z) shows a ∼ 2σ deviation from ΛCDM. At low redshifts, the results depend on the SNIa sample: CMB+DESI and CMB+DESI+PP yield β(z) consistent with zero within 2σ, while CMB+DESI+DESY5 and CMB+DESI+Union3 prefer negative β at ∼ 2σ. Both χ 2 tests and Bayesian analyses favor the β(z) model, with CMB+DESI DR2+DESY5 showing the most significant support through the largest improvement in goodness of fit (Δχ 2 MAP = -17.76) and strongest Bayesian evidence (lnℬ = 5.98 ± 0.69). Principal component analysis reveals that the data effectively constrain three additional degrees of freedom in the β(z) model, accounting for most of the improvement in goodness of fit. Our results demonstrate that the dynamical dark energy preference in current data can be equally well explained by such a sign-reversal interacting dark energy, highlighting the need for future observations to break this degeneracy.

It has been previously shown that multidimensional [Formula: see text] gravity can lead to a two-brane structure. In this paper, we analyze such a model with a spatially flat 4D de Sitter (dS) cosmology whose Hubble parameter H determines the universal energy scale. We show that the two-brane metric is nucleated at the highest energies. The distance between the branes grows gradually as the energy decreases, tending to a finite value at zero energy density. It is stated that the physical parameters such as the 4D Planck mass, the Higgs vacuum expectation value, and vacuum energy density vary with the evolving universal energy scale, even on the classical level. We also show that the Higgs vacuum expectation value is different on different branes.

It is shown to all orders of perturbation theory that in the effective field theory of general relativity the condition of vanishing of the vacuum energy leads to the same value of the cosmological constant viewed as a parameter of the effective Lagrangian, as obtained by demanding the consistency of the effective field theory in the Minkowski background. The resulting effective action is characterized by the cosmological constant term that vanishes exactly.

Conversely to widespread popular belief, different elder and newly established theories, including quantum mechanics, the theory of relativity, and of quantum vacuum, are not satisfactory in giving an account for different experimentally observed physical effects. This is considering that the corresponding physical qualitative description of observed effects, has not to be confused with its Mathematical-Physics treatment, which provides some virtual hypothetical statements. To be mentioned in a first step, the solid-state material physics and the undetermined time/location of quantum states, concerning the interpretation of the Raman effect, of Superconductivity and Semiconducting properties and of some endothermal material phase transitions of better performing advanced carbon materials which can then be used for many more demanding solid-state optoelectronic and mechanical applications, including the determination of the carbon phase content of asteroid providing improved knowledge on their origin. With the next steps, we discuss the validity of the developed theories of relativity and of quantum vacuum energy, referring to identified anomalies concerning the fundamentals of the optical properties of light, the description of the particle/wave duality, and the interpretation of the Doppler effect, and about the deflection of a light beam by some celestial bodies. All these, coming out to the rejection of the theoretical mathematical concept of the Space/Time curvature, and to some rehabilitation of the absolute Aether with newly defined specific properties. Last one, suggested to give account for several observed physical effects to be better complete interpreted, and particularly concerning the entanglement of distant subatomic particles, the interference pattern of discontinuously emitted single particles through young slits and the propagation speed of the light and of gravity waves which is suggested to be not constant, and which are opening new perspectives for an improved knowledge of the Universe.

This article presents a complete classification of Ricci solitons and their associated vector fields in the context of locally rotationally symmetric (LRS) Bianchi type I spacetime, a crucial model in cosmological studies. To systematically address the complexities inherent in the Ricci soliton equations, we adopt the Rif tree technique. The equations defining the Riccisoliton and its vector field are transformed into a reduced involutive form using a computational algorithm, which assists in dividing the integration process into a collection of cases organized in a tree-like structure. Each of these cases is governed by specific constraints on the metric functions, which facilitates the solution process. Definite expressions for the metric functions and the corresponding vector field of the Ricci soliton are obtained by efficiently solving the system of equations characterizing the soliton vector field through the application of these constraints. This powerful approach enables us to derive novel and exact solutions that previous methods have overlooked. Our results demonstrate that this spacetime admits Ricci solitons of shrinking, steady, and expanding natures, characterized by vector fields with up to 11 free parameters. Crucially, we conduct a thorough physical analysis of the resulting models, determining their matter content through the equation of state and testing their physical viability via the standard energy conditions. We find specific families of solutions that correspond to physically significant scenarios, such as a spacetime filled with vacuum energy (a cosmological constant). This work not only provides a comprehensive mathematical classification but also establishes a direct link between these geometric structures and potentially realistic cosmological models.

Abstract In this paper, we investigate quasinormal modes (QNMs) and greybody factors within the framework of Symmergent gravity, an emergent gravity model with an $$R + R^2$$ R + R 2 curvature sector. Building on our previous work on static spherically-symmetric solutions [Puliçe et al. in Class Quantum Gravity 40(19):195003, 2023], we explore the effects of the key parameters, including the quadratic curvature coupling parameter $$c_\textrm{O}$$ c O and the vacuum energy parameter $$\alpha $$ α . For all the three perturbations considered here viz., scalar, electromagnetic and gravitational perturbations, an increase in $$\alpha $$ α leads to a nearly linear rise in both oscillation frequencies and damping rates. The other parameter $$c_\textrm{O}$$ c O affects the QNMs spectrum nonlinearly. Additionally, the charge Q of the black hole introduces nonlinear behavior, where higher charges amplify the black hole’s electromagnetic field, resulting in increased oscillation frequencies and faster stabilization. These findings enhance our understanding of charged black hole stability and gravitational wave astrophysics. Further, the analysis of greybody factors reveals that increasing $$\alpha $$ α , $$c_\textrm{O}$$ c O , and Q reduces the absorption of radiation, with gravitational perturbations reaching maximum absorption at slightly lower frequencies compared to electromagnetic and scalar perturbations.

We propose a new UV-complete dark energy model which is neither a cosmological constant nor a slowly rolling scalar field. Our dark energy is the flux of a top form in a hidden sector gauge theory similar to QCD. The top form controls the vacuum energy generated by dark sector CP violation. Its flux discharges by the nucleation of membranes that source it. The tension and charge of the membranes are set by the chiral symmetry breaking scale ∼ 10-3 eV, and the dark energy is a transient. It decays on the order of the current age of the universe. The decays decrease dark energy discretely and randomly, instead of gradually like rolling scalars. Since the decay rate is close to the present Hubble scale, Γ ≳ H 0 4, in a time ∼ 𝒪(1/H 0) the cosmic acceleration may even cease altogether.