De Sitter

This paper presents the Theory of Relative Spatial Compression (RSC), a speculative hypothesis that proposes an alternative interpretation of cosmic expansion and redshift phenomena.
While the standard ΛCDM model attributes the accelerated expansion of the universe to dark energy, the RSC suggests that space itself may undergo nonlinear compression relative to an observer.
According to this model, distances between celestial objects could appear stretched due to observer-dependent spatial metrics rather than an intrinsic expansion of spacetime.

The idea originated from an early intuitive notion that space might not be uniform but dynamically compressed along the line of sight — a concept now explored in a physically consistent framework.
The theory aims to examine whether such relative compression could account for a portion of the observed cosmological redshift and offer an alternative to the dark-energy paradigm.
Although highly speculative and not empirically verified, the RSC serves as a conceptual framework designed to stimulate discussion about observer-dependent geometries and the structure of spacetime itself.

Cosmology today is confronted with several seemingly insoluble puzzles and strange, inexplicable coincidences. But a careful re-examination of the Cosmological principle and the Weyl postulate, foundational elements in this subject, suggests that we may be missing the point. The observations actually reveal a simpler and more elegant Universe than anyone could have imagined. The polish priest Nicolaus Copernicus (1473-1543) started a revolution with his heliocentric cosmology that displaced the Earth from the center of the Universe. His remarkable shift in paradigm continues to this day, the cornerstone of a concept we now call the Cosmological Principle, in which the Universe is assumed to be homogeneous and isotropic, without a center or boundary. But few realize that even this high degree of symmetry is insufficient for cosmologists to build a practical model of the Universe from the equations of General Relativity.

I propose a conceptual model , The Knit Entangled Model(KEM) of black holes, in which black holes are neither singularities of infinite density, nor tears in fabric of spacetime, but rather single, maximally entangled states. In this view, the spacetime doesn't break down; it condenses into a highly entangled "knot", preserving all the information about infalling matter. Hawking Radiation is interpreted as the gradual release of entanglement, ensuring information is never destroyed. This hypothesis offers a simple, intuitive framework that resolves the black hole information paradox while also connecting naturally with modern ideas such as AdS/CFT correspondence, ER=EPR, and quantum error correction.

We obtain (3+1) and (3+2) dimensional global flat embeddings of (2+1) uncharged and charged black strings, respectively. In particular, the charged black string, which is the dual solution of the Banados-Teitelboim-Zanelli black holes, is shown to be embedded in the same global embedding Minkowski space structure as that of the (2+1) charged de Sitter black hole solution.

We study the spectrum of gravitational perturbations around a vacuum de Sitter brane in a 5D asymmetric braneworld model, with induced curvature on the brane. This generalises the stealth acceleration model proposed by Charmousis, Gregory and Padilla (CGP) which realises the Cardassian cosmology in which power law cosmic acceleration can be driven by ordinary matter. Whenever the bulk has infinite volume we find that there is always a perturbative ghost propagating on the de Sitter brane, in contrast to the Minkowski brane case analysed by CGP. We discuss the implication of this ghost for the stealth acceleration model, and identify a limiting case where the ghost decouples as the de Sitter curvature vanishes.

This thesis is devoted to studying two important aspects of braneworld physics: their cosmology and their holography. We examine the Einstein equations induced on a general (n -2)-brane of arbitrary tension, embedded in some n-dimensional bulk. The brane energy-momentum tensor enters these equations both linearly and quadratically. From the point of view of a homogeneous and isotropic brane we see quadratic deviations from the FRW equations of the standard cosmology. There is also a contribution from a bulk Weyl tensor. We study this in detail when the bulk is AdS-Schwarzschild or Reissner-Nordström AdS. This contribution can be understood holographically. For the AdS-Schwarzschild case, we show that the geometry on a brane near the AdS boundary is just that of a radiation dominated FRW universe. The radiation comes from a field theory that is dual to the AdS bulk. We also develop a new approach which allows us to consider branes that are not near the AdS boundary. This time the dual field theory contributes quadratic energy density/pressure terms to the FRW equations. Remarkably, these take exactly the same form as for additional matter placed on the brane by hand, with no bulk Weyl tensor. We also derive the general equations of motion for a braneworld containing a domain wall. For the critical brane, the induced geometry is identical to that of a vacuum domain wall in (n-1)-dimensional Einstein gravity. We develop the tools to construct a nested Randall-Sundrum scenario whereby we have a "critical" domain wall living on an anti-de Sitter brane. We also show how to construct instantons on the brane, and calculate the probability of false vacuum decay.

We evaluate the one-graviton loop contribution to the vacuum polarization on de Sitter background in a 1-parameter family of exact, de Sitter invariant gauges. Our result is computed using dimensional regularization and fully renormalized with BPHZ counterterms, which must include a noninvariant owing to the time-ordered interactions. Because the graviton propagator engenders a physical breaking of de Sitter invariance two structure functions are needed to express the result. In addition to its relevance for the gauge issue this is the first time a covariant gauge graviton propagator has been used to compute a noncoincident loop. A number of identities are derived which should facilitate further graviton loop computations.

We investigate the D-brane bound states from the viewpoint of the unstable D/\bar{D}-system and their tachyon condensation. We consider two systems; a system of k D(-1)-branes and N D3-branes with open strings connecting them and a system of N D3-branes with open strings corresponding to the k-instanton flux, both of which are realized through the tachyon condensation from (N+2k) D3-branes and 2k \bar{D3}-branes with appropriate tachyon profiles. It can be shown that these systems are related with each other through a unitary gauge transformation of the D3/\bar{D3}-system. We construct an explicit form of the gauge transformation and show that the essential elements of the ADHM construction naturally arise from the explicit form of the gauge transformation. As a result, the ADHM construction is understood as an outcome of this gauge equivalence in different low energy limits. The small instanton singularities can be also understood in this context. Other kinds of solitons with diffe...

In recent years, a growing momentum has been gained by the emergent gravity framework. Within the latter, the very concepts of geometry and gravitational interaction are not seen as elementary aspects of Nature but rather as collective phenomena associated to the dynamics of more fundamental objects. In this paper we want to further explore this possibility by proposing a model of emergent Lorentzian signature and scalar gravity. Assuming that the dynamics of the fundamental objects can give rise in first place to a Riemannian manifold and a set of scalar fields we show how time (in the sense of hyperbolic equations) can emerge as a property of perturbations dynamics around some specific class of solutions of the field equations. Moreover, we show that these perturbations can give rise to a spin-0 gravity via a suitable redefinition of the fields that identifies the relevant degrees of freedom. In particular, we find that our model gives rise to Nordström gravity. Since this theory is invariant under general coordinate transformations, this also shows how diffeomorphism invariance (albeit of a weaker form than the one of general relativity) can emerge from much simpler systems.

This paper provides the ultraviolet (UV) completion of the Rupture–Containment Cosmology (RCC) framework. Building on the RCC Companion (technical Hilbert space foundations) and the RCC Cosmology paper (phenomenology and predictions), this work focuses on the most difficult corner of the Bronstein cube: (ℏ,c,G)
We present renormalization procedures, counterterms, and fixed-point structures, demonstrating that RCC is UV complete and consistent across all energy scales.

We introduce the S M Nazmuz Sakib Causal-Diamond Isoperimetric Law and the associated Sakib constants as a concise packaging of known small-diamond geometry in general relativity. For a 4D spacetime and a timelike geodesic observer with 4-velocity u a , we study the isoperimetric observable S(τ) = A(τ) 2 /V (τ) A0(τ) 2 /V0(τ) for a causal diamond of duration τ ; here (A 0 , V 0) denote Minkowski benchmarks of the same τ. We show that, as τ → 0, the expansion S(τ) = 1 + τ 2 κ 1 R ab u a u b + κ 2 R + O(τ 3) is universal and independent of the Weyl tensor at order τ 2 , in agreement with the analytic framework of small causal diamonds [1, 2, 3, 4]. With the convention above, the Sakib constants take the values κ 1 =-1 72 and κ 2 =-1 18 , which we verify numerically via correctly constructed null-boundary diamonds in FRW (conformal time), Schwarzschild, and Kottler (Schwarzschild-de Sitter) spacetimes, extending and systematizing computational checks previously scattered in the literature. We also clarify how alternative normalizations (e.g. using different S or boundary constructions) map to different coefficient pairs, resolving common sign/magnitude confusions. The work frames a reproducible numerical protocol that can serve as a benchmark for codes dealing with null congruences and small-set geometry.

The infinity paradox in black holes-where curvature invariants diverge and Hawking radiation demands unphysical negative energy flux-has long challenged classical and semiclassical physics. In parallel, the Standard Model treats the strong and weak forces as disjoint, yet experimental puzzles such as neutrino mixing and baryon stability hint at hidden overlaps. In this work we resolve both issues within the NJ0000 framework of Unsignificant Genesis (UG). By modeling overlapping causal sets in black hole interiors, we induce a variable light-speed field c(x) that regularizes curvature and renormalized stress tensors, eliminating singularities. In nuclear physics, we construct an abductive inference of a third, supra-strong operator from the overlap of the first (strong) and second (weak) forces, which patches structural gaps in the Standard Model. Together, these results substantiate the UG thesis that infinities are projection artifacts of SI-units, and vanish when dynamics are expressed in overlap-aware variables. Our work extends and builds upon recent investigations of overlapping causal sets in black hole interiors [7].

We introduce the µ-VMT transistor (Vacuum-Mediated Momentum Transistor), a novel quantum electronic device in which electrons traverse a vacuum gap and couple directly to quantum vacuum fluctuations. Unlike conventional tunneling devices or Josephson junctions, the µ-VMT exploits the vacuum not as a passive barrier but as an active mediator, entangling electron momentum with inaccessible vacuum modes. This entanglement leads to measurable anomalous momenta in transmitted electrons. We propose a Lagrangian framework in which the µ-VMT acts as the momentum dual of the Josephson junction, extending vacuum-assisted coherence from phase to momentum space. Possible realizations and experimental signatures are discussed, including implications for quantum information science and exotic metric-engineering concepts.

The recent discovery by of spiral patterns in the quasinormal modes (QNMs) of black hole ringdowns, detected via exact WKB analysis, suggests a geometric substructure in spacetime. This paper proposes that these spiral geometries are a macroscopic manifestation of the Helix-Light-Vortex (HLV) theory's spiral time, modeled as ψ(t) = t + iϕ(t) + jχ(t). We derive the spiral QNM patterns using a spiral-time-weighted Lagrangian and modified propagators embedded in a quasicrystalline spacetime lattice. The model predicts specific frequency shifts and sideband amplitudes in gravitational wave spectra, testable with LIGO/Virgo data. In the linear-time limit, the framework reduces to standard general relativity (GR) and quantum field theory (QFT), ensuring compatibility with established physics. This work elevates HLV from a theoretical proposal to an experimentally grounded paradigm.

The physics community has adopted the principle that when new experimental data appears, physicists should first try to explain it based on existing science. Only if all such attempts fail can new exotic explanations be brought in. However, in the case of cosmological acceleration, the opposite approach was taken: without serious attempts to explain this phenomenon from existing science, physicists attracted dark energy and other exotic concepts whose physical meaning is a mystery. As shown in our publications, the cosmological acceleration can be clearly explained without uncertainties. The derivation of this explanation requires significant technical efforts described in our publications. The purpose of this article for the 2nd International Conference on Gravitation, Astrophysics and Cosmology (ICGAC 2026) is to explain our approach at the simplest possible level so that the basic ideas of our approach would be understandable to many physicists and astrophysicists.

The Wavy Universe Consciousness Cycle (WUCC) and Binary Paradox Theory propose a unified conceptual framework for understanding the structure and dynamics of the cosmos through the dual nature of consciousness and the binary foundations of universal reality. The WUCC describes existence as an oscillatory cycle in which consciousness, matter, and antimatter evolve within a wave-like continuum, governed by phases of expansion, contraction, and transformation. The Binary Paradox introduces a fundamental code—expressed as “1 0 1 0”—where duality (matter/antimatter, existence/non-existence, observer/observed) is resolved through paradoxical overlap. This overlap accounts for asymmetries in matter–antimatter distribution, the persistence of a 5% matter dominance, and the cosmic microwave background as a residual echo of annihilation. Together, the theories suggest that reality is not linear but recursive, encoded through paradoxical binaries that sustain universal cycles. By linking metaphysics with cosmology, the WUCC and Binary Paradox Theory aim to offer a novel perspective on the origin, structure, and evolution of the universe while positioning consciousness as a central, active principle in cosmic dynamics.

This work presents the first testable predictions of the Constitutive Flux (CF) framework, a constitutive reinterpretation of gravitation based on a universal medium. Building on the mathematical foundations and validation calculations, the paper translates CF equations into observable constraints.

Results include:

Post-Newtonian parameters (γ = 1, β = 1 + α₁χ + ½α₂χ²), consistent with Solar-System tests.

Solar-System validation: perihelion precession, light deflection, Shapiro delay.

Gravitational waves: tensor modes propagate at c with negligible dispersion.

Binary pulsars: δ_Q ≪ 10⁻³, dipole channel absent in minimal CF.

Pulsar timing arrays: prediction of a narrowband scalar resonance at Ω₀ ≈ nHz.

These predictions establish a clear roadmap for confronting the CF framework with observational data.

Originally published on Zenodo

The Anti-de Sitter/Conformal Field Theory (AdS/CFT) correspondence represents one of theoretical physics' most significant advances, establishing a precise duality between higher-dimensional gravitational bulk theories and lowerdimensional conformal field theories on their boundaries. We demonstrate that this correspondence, while computationally powerful, is not required as an independent postulate within Universal Emergence Dynamics (UED). UED derives both bulk and boundary behaviour from a single coherence field evolving in meta-time, where spacetime geometry and causal orientation emerge as projections from an entropic field rather than fundamental structures. By restoring the physical significance of negative causal orientations through cubic projection forms, UED recovers all principal AdS/CFT resultsbulk-to-boundary correlators, the Ryu-Takayanagi entanglement entropy relation, and bulk reconstruction-without requiring an independent holographic dictionary. We show that boundaries are interference zones of projection rather than ontologically distinct surfaces, addressing the conceptual tension surrounding holographic information encoding while preserving all computational advantages. The framework naturally extends to de Sitter spacetimes, recasting both AdS/CFT and dS/CFT as representational limits of the same projection dynamics. Holographic duality thus remains a powerful computational paradigm, but within UED it reflects projection geometry rather than an indispensable principle.

At the classical level the electromagnetic field can be well identified at the spatial infinity. Staruszkiewicz pointed out that the quantization of the electromagnetic field at spatial infinity is essentially unique and follows from the two fundamental principles: 1) gauge invariance and 2) canonical commutation relations for canonically conjugated generalized coordinates, and constructed a simple and mathematically transparent quantum theory of the Coulomb field, predicting (among other things) a relation between the theory of unitary representations of the SL(2, C) group and the fine structure constant. Until now this theory has stayed outside the main stream of the perturbative development in QED, mainly due to the unsolved infra-red-type (IR) problems in the perturbative approach. Recently however there has been performed a more careful analysis of free fields including the mass less free gauge fields, such as the electromagnetic potential field, their Wick and chronological products, which revealed the need for a more careful and white noise construction of these fields, and which opened a way to resolve IR problems (at least those which shows up at each order separately). Comparison of the perturbatively constructed field at spatial infinity with the quantum phase field of the Staruszkiewicz theory leads to the proof of universality of the unit of charge.

At the classical level the electromagnetic field can be well identified at the spatial infinity. Staruszkiewicz pointed out that the quantization of the electromagnetic field at spatial infinity is essentially unique and follows from the two fundamental principles: 1) gauge invariance and 2) canonical commutation relations for canonically conjugated generalized coordinates, and constructed a simple and mathematically transparent quantum theory of the Coulomb field, predicting (among other things) a relation between the theory of unitary representations of the $SL(2, \mathbb{C})$ group and the fine structure constant. Until now this theory has stayed outside the main stream of the perturbative development in QED, mainly due to the unsolved infrared-type (IR) problems in the perturbative approach. Recently however there has been performed a more careful analysis of mass less free gauge fields, such as the electromagnetic potential field, their Wick and chronological products, which re...

We present in this paper how the single-photon wave function for transversal photons (with the direct sum of ordinary unitary representations of helicity 1 and -1 acting on it) is subsumed within the formalism of Gupta-Bleuler for the quantized free electromagnetic field. Rigorous Gupta-Bleuler quantization of the free electromagnetic field is based on our generalization (published formerly) of the Mackey theory of induced representations which includes representations preserving the indefinite Krein inner-product given by the Gupta-Bleuler operator. In particular it follows that the results of Bia lynicki-Birula on the single-photon wave function may be reconciled with the causal perturbative approach to QED.

At the classical level the electromagnetic field can be well identified at the spatial infinity. Staruszkiewicz pointed out that the quantization of the electromagnetic field at spatial infinity is essentially unique and follows from the two fundamental principles: 1) gauge invariance and 2) canonical commutation relations for canonically conjugated generalized coordinates, and constructed a simple and mathematically transparent quantum theory of the Coulomb field, predicting (among other things) a relation between the theory of unitary representations of the $SL(2, \mathbb{C})$ group and the fine structure constant. Until now this theory has stayed outside the main stream of the perturbative development in QED, mainly due to the unsolved infra-red-type (IR) problems in the perturbative approach. Recently however there has been performed a more careful analysis of free fields including the mass less free gauge fields, such as the electromagnetic potential field, their Wick and chron...

Resumen Se examina la hipótesis de que los vacíos cósmicos pueden funcionar como corredores gravitacionales de baja resistencia para partículas y naves, favoreciendo el desplazamiento cosmológico eficiente. El marco teórico se apoya en la relatividad general y la física de la materia oscura, integrando modelos matemáticos actuales para cuantificar el potencial energético y la dinámica en regiones de baja densidad. Se propone una teoría articulada y testable para futuras simulaciones y estudios observacionales.

We are interested in extending operators defined on positive measures, called here transfunctions, to signed measures and vector measures. Our methods use a somewhat nonstandard approach to measures and vector measures. The necessary background, including proofs of some auxiliary results, is included.

Let's analyze each part: 1. Quantum behavior of gravity and space-time both are relative function: Quantum behavior of gravity and spacetime: Yes, this is precisely what Quantum Gravity (QG) aims to describehow gravity behaves at the quantum level, and how spacetime itself becomes a quantum entity at scales like the Planck length. Are relative functions: This phrase relative function isn't standard physics terminology. However, if we interpret relative in the way we've discussed before (i.e., dependent on context, scale, or emergent properties), then there's a strong argument to be made: Scale Dependence: The quantum behavior of gravity and spacetime is certainly scale-dependent. At macroscopic scales, it appears as classical General Relativity. At the Planck scale, it's expected to manifest entirely new quantum phenomena. In this sense, its function (how it behaves, how we describe it) is relative to the scale of observation. Emergent Relativity: Many QG theories propose that classical principles of relativity (like Lorentz invariance, smooth spacetime) are emergent properties, not fundamental ones. They would hold true only in certain situations (low energy, large distances). So, the fundamental quantum behavior might not strictly adhere to classical relativity, but give rise to it. In this sense, the quantum behavior is "relative" to the emergence of classical relativistic spacetime. So, if interpreted as scale-dependent, context-dependent, or related to the emergence of classical relativity, then this part has a strong conceptual basis in modern QG ideas.

This article establishes a parallel between Kosmos Theory and contemporary physics, in particular topological physics and the AdS/CFT holographic duality, proposing that life and consciousness be understood as topological phases of spacetime. These phases are sustained by Cosmological Consciousness (CC)the ontological foundation associated with the geometric volume of the cosmosand manifested in the nonorientable interface between mirror universes (matter and antimatter), modeled by the topology of the Klein bottle. The analysis takes as its starting point Wolfgang Pauli's famous phrase-"God made the volume; the surface was invented by the devil"reinterpreting it in cosmological, physical, and phenomenological terms. The volume (bulk) corresponds to the continuous domain of gravitational geometry, where Cosmological Consciousness resides as the stability of Being. The surface (boundary) corresponds to the holographic and informational domain, the paradoxical and creative locus where life, information, and embodied consciousness emerge. On this surface, the Unitary Phenomenal Self (UPS) manifests as a protected edge state, robust against local perturbations, analogous to Majorana modes in topological systems. The article integrates concepts from general relativity (gravity as geometric curvature), condensed matter physics (topological phases and edge states), black hole thermodynamics (horizons as informational surfaces), and AdS/CFT holography (bulkboundary). These physical references are articulated with contributions from Husserl and Merleau-Ponty's phenomenology (consciousness as experience of a boundary), Lupasco's logic of the included third (paradoxical interface of opposites), and the philosophy of Heidegger and Jung (ek-sistence and Unus Mundus). It concludes that consciousness should not be understood as a neurobiological epiphenomenon, but as a structural and topological dimension of the cosmos. Gravity curves the volume, life stabilizes the topological surface, and consciousness emerges as the holographic correlation between volume and surface. The UPS, as a topological Dasein, is the intersection where geometry, information, and sentience intertwine, making the cosmos capable of reflecting upon itself.

This article proposes the Hyper-Shell Universe, a novel anisotropic cosmological model where our cosmos, in its totality, exists as the dynamically expanding throat of an Einstein-Rosen bridge (wormhole), topologically connecting two conceptual black hole regions. This bridge is fundamentally a thick, finite spherical shell of uniformly distributed energy-matter (galaxies). This "pressureless dust" configuration results in an almost vacuum-like actual energy density, paralleling de Sitter spacetime. Despite its finite global extent, this wormhole throat appears boundless to internal observers due to its causally disconnected boundaries. Within this vast bridge, the observable universe for any observer is a small fragment, idealized as a finite-thickness planar slab that appears infinite in all three spatial dimensions. This perception is strongly reinforced by the Hubble rate's limits and the continuous, oscillatory curving of geodesics in the radial direction that hides its edges. Departing from the unconstrained, often unintuitive geometries of the prevailing \LambdaCDM model, the Hyper-Shell defines a universe with discernible global boundaries: inner and outer 3-spheres that function as the coinciding horizons of a Schwarzschild-de Sitter (SdS) metric, specifically the Nariai solution, analogous to the mouths of the wormhole. This inherent non-perceptibility-achieved through inward curving geodesics towards the bridge's central plane (where spacetime is locally near-flat, analogous to the throat's narrowest point) and an event horizon-like effect from the universe's prodigious cumulative mass-fosters an illusion of large-scale homogeneity and isotropy for all internal observers. Crucially, due to the intricate bending of light near these boundaries, every observer within the Hyper-Shell will perceive a perfectly spherical observable universe, entirely free of optical distortions, regardless of their radial position, as if projected from its holographic boundaries. This perception is further reinforced by an invariant relationship where the size of any observer's observable universe remains precisely equal to the Schwarzschild radius of its contained mass. This concept positions the Hyper-Shell Universe as an expanding cosmic structure bounded by effective event horizons that act as holographic screens. This unique spatial configuration, coupled with an intrinsically derived gravitational potential (quadratic in radial distance within the observable slab approximation), offers robust resolutions to several persistent cosmological puzzles, including the Cosmic Microwave Background's paradoxical uniformity, its anomalous dipole, the quasar dipole, the Hubble tension, the S8 tension, the CMB Cold Spot, the phenomenon of large-scale bulk flows, the small-scale dark matter problems (cuspy halo, missing satellites), the Lithium problem, cosmic ray anisotropies, the "Axis of Evil," the Lyman-alpha forest variations, the Pioneer anomaly, the information paradox, and the fundamental question of cosmic boundaries and the darkness of the night sky (Olbers' Paradox). These observed anisotropies and tensions, particularly their consistent yet varying magnitudes and directional alignment, provide crucial evidence suggesting our specific radial location within a "thin" Hyper-Shell, making them natural predictions. The model also reinterprets dark energy as an intrinsic, dynamically influenced repulsive property of matter, providing a unified physical basis for cosmic expansion and resolving the cosmological constant and coincidence problems. This dark energy interpretation finds conceptual resonance with discussions in modified gravity, emergent gravity, and backreaction theories, all of which explore acceleration driven by properties tied to spacetime geometry or matter distribution. By presenting a geometrically tangible and causally contained universe that appears infinitely boundless and uniformly spherical to all internal observers, the Hyper-Shell provides a coherent and accessible narrative for cosmic expansion and observable phenomena, all grounded firmly in established fundamental physics.

I present a complete formulation of the zero-point field as the hydrodynamic ground state of a fifth-dimensional temporal medium that I call the chronoflux. In my framework, fluctuations of the chronoflux generate the measurable phenomena that are normally attributed to quantum vacuum fluctuations. I write a five-dimensional action whose variation yields a coupled system for gravity, the chronoflux field, and an informational scalar that encodes resistance to information change. I derive the effective four-dimensional vacuum stress energy, show a selftuning prescription that preserves local Lorentz symmetry while allowing a small effective cosmological constant, and compute Casimir energy including leading corrections from slowly varying temporal flow. I propose differential experiments in superconducting cavities, Josephson-cavity cross checks, atom interferometry, and Casimir-Polder mapping. Appendices provide sign conventions, unit checks, and the reduction steps.

Finite part integrals are core to the theory of regularizations, vital for modern physics by assigning finite values to divergent expressions, but they tend to require polynomial divergence or a nice analytic continuation. This paper has the purpose to derive a way to evaluate fp integrals of any growth using ideas from Fourier analysis \& distribution theory applied to asymptotic behavior.

In this paper we analyze the impact of stair-step incentive schemes, commonly used in the automotive industry, on both expected sales and sales variability. We model the e¤ect of stair-step incentives in two speci…c scenarios: an exclusive dealership selling cars for only one manufacturer and a non-exclusive dealership selling cars for multiple manufacturers. For an exclusive dealer we show that appropriate stair-step incentives, with a positive bonus on crossing the threshold, not only increase the expected sales, but more importantly, decrease the coe¢ cient of variation of sales. We show that if the manufacturer associates a positive cost with sales variance, a stair-step incentive, with a positive bonus, is superior to the scheme without a bonus. We then show that manufacturers continuing to o¤er stair-step incentives to non-exclusive dealers experience an increase in variance and a decrease in pro…ts. This implies that when manufacturers must compete for dealer e¤ort, stair-step incentives can hurt manufacturers.

We consider in this work quantities that can be obtained as limits of powers of parametrized matrices, for instance the inverse matrix or the logarithm of the determinant. Under the assumption of affine dependence in the parameters, we use the Empirical Interpolation Method (EIM) to derive an approximation for powers of these matrices, from which we derive a nonintrusive approximation for the aforementioned limits. We derive upper bounds of the error made by the obtained formula. Finally, numerical comparisons with classical intrusive and nonintrusive approximation techniques are provided: in the considered test-cases, our algorithm performs well compared to the nonintrusive ones.

We propose a semiclassical method to calculate S–matrix elements for two– stage gravitational transitions involving matter collapse into a black hole and evaporation of the latter. The method consistently incorporates back–reaction of the collapsing and emitted quanta on the metric. We illustrate the method in several toy models describing spherical self–gravitating shells in asymptotically flat and AdS space–times. We find that electrically neutral shells reflect via the above collapse–evaporation process with probability exp(−B), where B is the Bekenstein–Hawking entropy of the intermediate black hole. This is consistent with interpretation of exp(B) as the number of black hole states. The same expression for the probability is obtained in the case of charged shells if one takes into account instability of the Cauchy horizon of the intermediate Reissner–Nordström black hole. Our semiclassical method opens a new systematic approach to the gravitational S–matrix in the non–perturbat...

We study the horospherical geometry of submanifolds in hyperbolic space. The main result is a formula for the total absolute horospherical curvature of M, which implies, for the horospherical geometry, the analogues of classical inequalities of the Euclidean Geometry. We prove the horospherical Chern-Lashof inequality for surfaces in 3-space and the horospherical Fenchel and Fary-Milnor's theorems.

This work proposes falsifiable astrophysical predictions-namely, enhanced antimatter-to-matter emission ratios and gammaray spectral suppression near extreme gravitational singularities-based on the Irreversible Informational Structure (IIS) framework. The observational targets include specific energy signatures detectable by instruments such as Fermi-LAT, AMS-02, and HESS. The IIS framework redefines "information" not as syntactic entropy or probabilistic data, but as an observer-dependent epistemic structure encoding the irreversibility of physical evolution. At its core lies the third-rank informational tensor T ijk (x, U), describing directed, asymmetric flows of epistemic content in curved spacetime. By analytically investigating the Tomimatsu-Sato (TS2) solution, we demonstrate that strong informational gradients-captured by ∇ k T k ij-can act as cognitive compression zones where matter-antimatter asymmetry emerges. The black hole thus operates as an entropy sink, while its white hole counterpart becomes an epistemically reconstructed domain emitting antimatter. This paper represents a novel step toward a unified understanding of black hole thermodynamics, information flow, and antimatter genesis, offering a concrete observational gateway into the epistemic-informational duality of the universe.

**Preprrint

We find various asymptotic limits of universes containing two interacting fluids which interact and exchange energy. We study the finite-time singularities that may develop in these cosmologies and obtain the asymptotic behaviours of the solutions near such blow up regimes.

We find various asymptotic limits of universes containing two interacting fluids which interact and exchange energy. We study the finite-time singularities that may develop in these cosmologies and obtain the asymptotic behaviours of the solutions near such blow up regimes.

We propose a new interpretation of Hawking radiation based on Vortex Field Theory. Infalling matter triggers quantum vortex instabilities near the event horizon, leading to informationcarrying radiation. This mechanism offers a non-thermal, phasedriven explanation for black hole emission and provides a potential resolution to the black hole information paradox.

Locality of interactions is an essential ingredient of Special Relativity. Recently, a new framework under the name of relative locality has been proposed as a way to consider Planckian modifications of the relativistic dynamics of particles. We note in this paper that the loss of absolute locality is a general feature of theories beyond Special Relativity with an implementation of a relativity principle. We give an explicit construction of such an implementation and compare it both with the previously mentioned framework of relative locality and the so-called Doubly Special Relativity theories.

This speculative paper proposes that time and energy are fundamentally equivalent, a hypothesis inspired by philosophical discourse and Einstein's theory of relativity. We outline a conceptual framework suggesting that temporal progression may be a manifestation of energy, deriving from the transformation of a pre-temporal state at the Big Bang. Implications for cosmology, quantum mechanics, and thermodynamics are discussed, alongside preliminary mathematical formulations. We conclude by proposing experimental approaches to validate this principle.

A well known example in quantum electrodynamics (QED) shows that Coulomb scattering of unpolarized electrons, calculated to lowest order in perturbation theory, yields a results that exactly coincides (in the non-relativistic limit) with the Rutherford formula. We examine an analogous example, the classical and perturbative quantum scattering of an electron by a magnetic field confined in an infinite solenoid of finite radius. The results obtained for the classical and the quantum differential cross sections display marked differences. While this may not be a complete surprise, one should expect to recover the classical expression by applying the classical limit to the quantum result. This turn not to be the case. Surprisingly enough, it is shown that the classical result can not be recuperated even if higher order corrections are included. To recover the classic correspondence of the quantum scattering problem a suitable non-perturbative methodology should be applied.

We consider entanglement harvesting in de Sitter space using a model of multiple qubit detectors. We obtain the formula of the entanglement negativity for this system. Applying the obtained formula, we find that it is possible to access to the entanglement on the super horizon scale if a sufficiently large number of detectors are prepared. This result indicates the effect of the multipartite entanglement is crucial for detection of large scale entanglement in de Sitter space.

The geodesics of a spacetime seldom coincide with those of an embedded submanifold of codimension one. We investigate this issue for higher-dimensional general relativity-like models, firstly in the simpler case without branes to isolate which features are already present, and then in the more complicated case with branes. The framework in which we consider branes is general enough to include asymmetric braneworlds but not thick branes. We apply our results on geodesics to study both the equivalence principle and cosmological singularities. Among the models we study these considerations favour Z 2 symmetric braneworlds with a negative bulk cosmological constant.

We generalise Wesson's procedure, whereby vacuum (4 + 1)-dimensional field equations give rise to (3 + 1)-dimensional equations with sources, to arbitrary dimensions. We then employ this generalisation to relate the usual (3 + 1)-dimensional vacuum field equations to (2 + 1)-dimensional field equations with sources and derive the analogues of the classes of solutions obtained by Ponce de Leon. This way of viewing lower dimensional gravity theories can be of importance in establishing a relationship between such theories and the usual 4-dimensional general relativity, as well as giving a way of producing exact solutions in (2 + 1) dimensions that are naturally related to the vacuum (3 + 1)-dimensional solutions. An outcome of this correspondence, regarding the nature of lower dimensional gravity, is that the intuitions obtained in (3 + 1) dimensions may not be automatically transportable to lower dimensions. We also extend a number of physically motivated solutions studied by Wesson and Ponce de Leon to (D + 1) dimensions and employ the equivalence between the (D + 1) Kaluza-Klein theories with empty D-dimensional Brans-Dicke theories (with ω = 0) to throw some light on the solutions derived by these authors.

The general classical solution of the 3D electromagnetic pp-wave spacetime has been obtained. The relevant line element contains an arbitrary essential function providing an infinite number of in-equivalent geometries as solutions. A classification is presented based on the symmetry group. To the best of our knowledge, the solution corresponding to only one of the Classes is known. The dynamics of some of the Classes was also derived from a minisuperspace Lagrangian which has been constructed. This Lagrangian contains a degree of freedom (the lapse) which can be considered either as dynamical or non-dynamical (indicating a singular or a regular Lagrangian correspondingly). Surprisingly enough, on the space of classical solutions, an equivalence of these two points of view can be established. The canonical quantization is then used in order to quantize the system for both the singular and regular Hamiltonian. A subsequent interpretation of quantum states is based on a Bohm-like analysis. The semi-classical trajectories deviate from the classical only for the regular Hamiltonian and in particular for a superposition of eigenstates (a Gaussian initial state has been used). Thus, the above mentioned equivalence is broken at the quantum level. It is noteworthy that the semi-classical trajectories tend to the classical ones in the limit where the initial wavepacket is widely spread. Hence, even with this simple superposition state, the classical solutions are acquired as a limit of the semi-classical.

A comparison between the line of sight power spectrum (the auto spectrum) of absorption in the Lyman-alpha forest and the cross power spectrum (the cross spectrum) between the absorption in neighboring lines of sight offers an evolution-free means to constrain the cosmological constant, or dark energy. Using cosmological simulations, we consider a maximum likelihood method to obtain constraints from this comparison. In our method, measurements of the auto and cross spectra from observations are compared with those from a multi-parameter grid of simulated models of the intergalactic medium (IGM). We then marginalize over nuisance parameters to obtain constraints on the cosmological constant. Redshift space distortions due to peculiar velocities and thermal broadening, a potential difficulty in applying this test, are explicitly modeled in our simulations. To illustrate our method, we measure the cross spectrum from a new sample of five close quasar pairs, with separations of 0.5 to 3 arcmin. Using published measurements of the auto spectrum and our measurements of the cross spectrum, we attempt to obtain a constraint on Ω Λ , but find only weak constraints. An Einstein-de-Sitter cosmology is, however, disfavored by the data at a ∼ 2σ confidence level. We consider the power of future observations, paying particular attention to the effects of spectral resolution and shot-noise. We find that ∼ 50 moderate resolution, FWHM ∼ 150 km/s, fully-overlapping, close separation pairs (with ∆θ ∼ 30 ′′ -120 ′′ ) should allow a (2σ) constraint on Ω Λ at the level of 15%, if other modeling parameters are well determined through other means. We find that there is a sizeable gain from observing very close, ∆θ ∼ 30 ′′ , separation pairs provided they are observed with high spectral resolution. A sample of ∼ 10 such pairs would yield similar constraints to the 50 moderate resolution pairs mentioned above.

We investigate linearized gravity on a single de Sitter brane in the anti-de Sitter (AdS) bulk in the Einstein Gauss-Bonnet (EGB) theory. We find that Einstein gravity is recovered for a high energy brane, i.e., in the limit of a large expansion rate, i.e., for H 1, where H is the de Sitter expansion rate and is the curvature radius of the AdS bulk. We also show that, in the short distance limit, r min{ , H -1 }, Brans-Dicke gravity is obtained, whereas in the large distance limit, r max{ , H -1 }, a Brans-Dicke-type theory is obtained for H = O(1), and Einstein gravity is recovered both for H 1 and H 1. In the limit H → 0, these results smoothly match the results known for the Minkowski brane.

The radion on the de Sitter brane is investigated at the linear perturbation level, using the covariant curvature tensor formalism developed by Shiromizu, Maeda and Sasaki. 1) It is found that if there is only one de Sitter brane with positive tension, there is no radion, and thus ordinary Einstein gravity is recovered on the brane, with the exception of corrections due to the massive Kaluza-Klein modes. As a by-product of the covariant curvature tensor formalism, it is immediately seen that cosmological scalar, vector and tensor type perturbations all have the same Kaluza-Klein spectrum. On the other hand, if there are two branes, one with positive tension and another with negative tension, the gravity on each brane receives corrections from the radion mode in addition to the Kaluza-Klein modes, and the radion is found to have a negative mass-squared proportional to the curvature of the de Sitter brane. This is in contrast to the flat brane case, in which the radion mass vanishes and becomes degenerate with the 4-dimensional graviton modes. To relate our result with the metric perturbation approach, we derive the second-order action for the brane displacement. We find that the radion identified in our approach indeed corresponds to the relative displacement of the branes in the Randall-Sundrum gauge and describes the scalar curvature perturbations of the branes in Gaussian normal coordinates around the branes. The implications of our results with regard to the inflationary brane universe are briefly discussed.