Papers

The gravitational influence of dark matter (DM) halos on the strong-field regime around supermassive black holes (SMBHs) remains largely unexplored. In the present work, we try to make a framework of the halo-modified space times for four well-known DM profiles including the Navarro Frenk-White (NFW), Moore, Burkert, and Dehnen-(1,4,3/4) profiles, respectively. We derive the corresponding photon spheres, shadow radii, and innermost stable circular orbits (ISCO) for the Sgr A* and M87*. We then constrain the DM halo parameters by comparing the theoretical values with the observed Event Horizon Telescope (EHT) data, and the robustness was checked by comparing the obtained virial mass of the Milky Way and M87 from the parameters with the values already present in the literature. In addition to this we extend the geodesic analysis by formulating the perturbed orbital dynamics using a Painlevé-Gullstrand Hamiltonian framework, and as a result we compute orbital trajectories, Poincaré sections, and finite-time Lyapunov ex ponents. These chaotic dynamics leave distinct imprints on gravitational waveforms, including phase irregularities and amplitude modulations.

We investigate the linear perturbation cosmology of a spinor-field realization of quintessence dark energy by implementing the model in the Einstein–Boltzmann solver CLASS. The model parameters are constrained using a Markov Chain Monte Carlo analysis with Pantheon$^{+}$ Type Ia supernovae, cosmic chronometers, DESI DR2 baryon acoustic oscillations, redshift-space distortions, and Planck 2018 CMB distance-prior data. For the full combined dataset, we obtain $w_{\rm de}=-0.9710^{+0.0206}_{-0.0206}$, $\Omega_{m0}=0.2939^{+0.0047}_{-0.0047}$, and $H_0=66.23^{+0.55}_{-0.53},\mathrm{kms^{-1}Mpc^{-1}}$. The corresponding perturbation quantities are $\sigma_8=0.7537^{+0.0076}_{-0.0075}$ and $S_8=0.7459^{+0.0067}_{-0.0065}$. We find that the spinor-quintessence model closely reproduces the predictions of a phenomenological constant-$w$ model in the matter power spectrum, growth-rate observable $f\sigma_8$, growth index, and CMB temperature anisotropy spectrum, with deviations generally below the percent level. A comparison with $\Lambda$CDM and $w$CDM shows statistically indistinguishable fits, although the Bayesian information criterion favors the simpler $\Lambda$CDM model. Our results demonstrate that the spinor-field quintessence scenario remains consistent with current expansion-history and structure-growth observations when its perturbation evolution is treated consistently, providing a field-theoretically motivated realization of constant-$w$ dark energy at the background and linear perturbation levels.

Inspired by the latest progress in the hunt of acceptable cosmological model of the universe, present paper is devoted to explore a mathematical model of the universe having initial anisotropy and with accelerated evolution that attains isotropic character. We have considered a widely accepted anisotropic Bianchi type I space-time geometry of the universe to explore a physically viable model. To find an acceptable model, we adopted a hyperbolic form for the scale factor as $ a(t)= \left( sinh bt \right)^{\frac{1}{n}} $ and a relation $ \Lambda=\Lambda_0 \frac{\ddot{a}}{a}$. The model parameters are constrained by $ \chi^2$ minimization techniques. Using 35 CC measurements we obtain present day expansion rate $H_0= 65.715 Km/S/Mpc$ and the value of $ n= 1.3024$. Further to estimate the local uncertainties of the best fit parameter, we calculate covariance from the Jacobin of the normalized residuals. The corresponding 1 $\sigma$ uncertainties are $ H_0=65.715 \pm 2.392 Km/S/Mpc$ and $n= 1.3024 \pm 0.0842$. The physical and dynamical behaviour of present model has been discussed by a graphical representation of cosmological parameters. The observational constraints on the expansion history are found to be consistent with a present accelerated phase and a transition from deceleration to acceleration at an intermediate redshift. The corresponding evolution of the derived cosmological quantities is also investigated within the adopted model.

This article presents a wormhole solution constructed from a generalized ghost dark energy (GGDE) source in general relativity. At first, a brief review of GGDE is presented along with the necessary mathematical frameworks. We employed the Markov Chain Monte Carlo (MCMC) technique to constrain the free parameters of the model using the CC+BAO, $Pantheon^+$, and their combined datasets. Furthermore, the Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) were used to statistically assess the model's performance and determine its level of acceptance. Next, the basics of wormhole geometries along with the thin-shell formalism are explained in detail. After that, three different wormhole solutions associated with three different choices of the redshift function are presented ,and their various geometric properties as well as energy conditions are studied graphically. Finally, the stability of these thin–shell structures is examined analytically as well as graphically by studying the associated effective potential.

We investigate black hole solutions in F(R) gravity within a four-dimensional spacetime, separately treating the cases of vanishing and nonvanishing energy momentum tensors. We demonstrate that in the absence of an energy momentum tensor, the number of independent equations is sufficient to obtain the Ricci flat solutions without the need for a prescribed F(R) function. In the same case, also the solutions with variable Ricci scalar can obtained too. Furthermore, for a nonvanishing energy momentum tensor, we derive exact solutions for both constant and variable Ricci scalars, thereby introducing new charged black holes. Utilizing this new method, we not only recover the general relativistic and previously known F(R) gravity solutions but also introduce four new classes of F(R) black holes. We calculate their thermodynamic quantities and confirm the validity of the first law of black hole thermodynamics. The thermal stability of these new black holes is analyzed using both thermodynamic and geometrical approaches. Finally, the photon spheres and black hole shadows are studied within the F(R) gravity framework.

Multiphase porous piezoelectric media are essential for advanced transducers and smart sensors. Existing theories typically postulate Newton's second law for each phase or rely on phenomenological Hamiltonian constructions. The former forces ad hoc virtual-mass tensors to describe interphase inertia, while the latter provides no intrinsic safeguard against thermodynamic inconsistency when piezoelectric and multiphase couplings are superposed. In this work, we establish a linear dynamic and constitutive theory for anisotropic multiphase porous piezoelectric media from global energy conservation (GEC). From an abstract energy density functional, Taylor expansion and symmetry constraints derive the standard kinetic and potential energy densities and electric enthalpy, rather than assuming them a priori. Localization of the GEC integral yields the multiphase momentum equations, Gauss's law, the coupled constitutive relations, and the boundary conditions as mathematical corollaries, without invoking Newton's law or Hamilton's principle. The framework eliminates virtual-mass parameters entirely: interphase inertial coupling emerges organically from the off-diagonal kinetic-energy coefficients $\rho_{ij}^{\alpha\beta}$. Because all coefficients derive from a single smooth potential, Schwarz's theorem automatically guarantees Maxwell reciprocity and full thermodynamic self-consistency. The formulations agree with those from Hamilton's principle and reduce exactly to Biot's poroelastic theory and Tiersten's single-phase piezoelectric theory in the respective limits. Finally, linear plane-wave analysis produces a generalized Christoffel eigenvalue equation, and numerical phase-velocity calculations for water-saturated porous PZT-2 illustrate the modal structures and reveal strongly directional electromechanical coupling.

Megawatt-class orbital data centers require continuous maintenance, replacement, inventory, and service capacity in addition to spacecraft power/thermal systems. We formulate an analytical lifecycle framework for permanent/transient failures, modular orbital replacement units, robotic servicing, spare inventory, scheduled technology refresh, correlated faults, cybersecurity, optional human support. The model combines nonhomogeneous component hazards, capacity-weighted availability, multiclass robotic-service capacity, Poisson base-stock inventory, replacement-flow accounting, human-support break-even relations. For a 1 MW cluster with 10 active 100 kW nodes, 1 reserve node, ~200 5 kW compute cartridges, low, nominal, high deployed-mass allocations span ~50-75 kg/kW. Assumptions yield 70.2 random or life-limited interventions and 323-349 planned refresh operations/(MW-year), for a total of 393-419 standardized operations/(MW-year). Analysis gives a first-generation logistics of 5.3-9.0 t/(MW-year), with a nominal case of ~ 6.6 t/(MW year), 560-700 productive robot-hors/(MW-year). Planned refresh exceeds random replacement under the stated component populations, hazards, 3-15-year intervals. At ~400 standardized operations/(MW-year), the post-internal-recovery exception probability is <$10^{-3}$, with an objective near $10^{-4}$ at large scale; terminal non-recovery $p_U$ requires a smaller mission-level allocation. The target catastrophic-loss hazard for a 100 kW node is 0.01-0.03 1/yr. Parametric workload and cost cases place contingency visits at 10s of MWs, periodic campaigns at 10-100s of MWs, dedicated personnel at several 100 MWs to GWs. The reference first deployment is uncrewed, autonomously fault-managed, robotically maintainable, supported by specific inventory based on a 6-month replenishment horizon, compatible with later human access without permanent habitation.

Exceptional deficiency is a newly discovered broadband non-Hermitian condition, at which the system's spectrum is entirely composed of exceptional points and all eigenvectors pairwise coalesce. Here, we analyze the steady-state and time-domain responses of non-Hermitian lattices at exceptional deficiency by considering their frequency and time-domain Green's functions. We show that the frequency-domain Green's functions are characterized by the emergence of second-order poles across the entire spectrum, producing broadband second-order super-Lorentzian line shapes, enhanced magnitude, and sequential 2pi phase shifts across each resonance. These second-order poles also underpin unconventional responses to global dissipation, by which we uncover a loss-revival of defective skin effect: the skin modes that are "missing" due to the system's defectiveness at exceptional deficiency can re-emerge in the responses. In the time-domain responses, a linear-in-time amplification factor is identified in the evolution kernel, which can enhance skin-effect dynamics that would otherwise be suppressed by global loss. The amplification strength scales with the degree of defectiveness of the system and diminishes upon spectral detuning between subsystems. Our work establishes a theoretical framework for analyzing steady-state and dynamic signatures of exceptional deficiency, and opens new routes for dissipation-controlled broadband exceptional responses.

We compare two thermodynamic prescriptions associated with the same static, spherically symmetric four-dimensional Einstein-Gauss-Bonnet anti-de Sitter black hole. Model A uses the usual Hawking temperature obtained from the surface gravity and consequently yields an entropy with a logarithmic correction. Model B preserves the shift symmetry of the scalar field at the level of the thermodynamic charges, recovers the Bekenstein-Hawking area law, and requires a modified temperature for consistency with the first law. We derive the equations of state, Gibbs free energies, heat capacities, and critical quantities of both prescriptions in the extended phase space. The two models display the same qualitative Van der Waals phase structure, but their critical scales and local stability regions differ quantitatively. In the uncharged case, Model A has a larger critical horizon radius and lower critical temperature and pressure than Model B.

We present a finite-domain inverse reconstruction of a Morris–Thorne-type wormhole candidate as a methodological benchmark for constrained numerical model building in modified gravity. The throat condition and local flare-out behaviour are embedded analytically in the shape-function parameterization, while the redshift profile is kept finite by construction. Rather than fitting $f(R)$, $f_R(R)$, and $f_{RR}(R)$ as independent numerical arrays, a positive analytic generator is assigned to $f_{RR}(R)$ and integrated to obtain a derivative-consistent reconstructed curvature sector. The frozen reconstruction is evaluated on 10,019 radial nodes over $r\in[1,10^{5}]$. The corresponding Ricci-scalar trajectory spans $-1.1317\times10^{-9}\leq R\leq1.999999998$ and is weakly non-monotonic, so no inversion $r=r(R)$ is required. On the same finite grid, the reconstructed source variables retain positive pointwise energy-condition margins, the coordinate-radial null-energy integrals are positive both globally and in the near-throat band, and the maximum normalized tidal-curvature ratio is $0.8666<1$. The reconstructed source-side closure diagnostic has a maximum absolute residual of $5.3246\times10^{-5}$. The source closure is phenomenological rather than derived from a unique microphysical matter Lagrangian or a uniquely specified curvature–matter coupling function. Accordingly, the result is not presented as a full field-equation solution of a specified nonminimally coupled $f(R)$ theory, a stability proof, an exterior-matched global spacetime, or an observer-dependent safe-traversal model. It instead provides a finite-domain computational benchmark for auditable inverse reconstruction of Morris–Thorne-type geometries in modified gravity.

We investigate the leading near-horizon response of Blandford-Znajek energy extraction to a compact, neutral spin-polarized source within minimally coupled Einstein-Cartan-Dirac-Maxwell theory. Eliminating the algebraic contortion yields an effective axial contact interaction, which we embed into a conserved, anisotropic phenomenological completion. Working at leading order in the torsion parameter $\epsilon_T$, spatial anisotropy $\xi$, and slow rotation $\chi=a/M$ on the fixed-ADM branch, we derive the modified energy extraction rate at optimal load. We find that the leading-order power ratio $P_{\rm BZ}^{\rm EC}/P_{\rm BZ}^{\rm K}$ receives distinct contributions from rotational dragging ($\ell=1$) and magnetostatic flux redistribution ($\ell=2$). In the isotropic limit ($\xi=0$), the power is enhanced for a co-rotating completion and suppressed for a counter-rotating one, whereas for $\xi\neq0$ the net shift depends on the polar quadrupole response. We also formulate the generalized Znajek identity and linearized Grad–Shafranov framework, demonstrating that undetermined load-factor shifts leave the leading power coefficient invariant due to stationarity at the matched load point.

We investigate the cosmological implications of the bulk viscosity within the framework of $f(R,T)$ gravity by considering the linear model $f(R,T)=R+2\lambda T$, where $\lambda$ characterizes the matter–geometry coupling. Assuming a homogeneous and isotropic Friedmann–Lemaître–Robertson–Walker Universe, we derive analytical expressions for the Hubble parameter in two different scenarios: model A, corresponding to a pressureless viscous fluid ($\omega=0$), and model B, where the equation of state (EoS) parameter is treated as a free parameter. The cosmological parameters are constrained through a Markov Chain Monte Carlo analysis. The results show that both viscous $f(R,T)$ models provide an excellent description of the current expansion history and remain compatible with the combined observational data. Model A is slightly favored over the standard cosmological model ($\Lambda$CDM) according to AICc, reflecting the improved fit achieved with only one additional free parameter. In contrast, the BIC continues to favor the simpler $\Lambda$CDM model owing to its stronger penalty on model complexity. Although model B yields the lowest minimum $\chi^2$, the improvement is too small to justify the introduction of an additional free parameter, resulting in a statistical performance comparable to $\Lambda$CDM according to the AICc but less favorable according to the BIC.

We propose a relational noncommutative framework in which quantum kinematics, semiclassical geometry, internal gauge structure, and ultraviolet fixed-point behaviour arise as sectors of a common $*$-algebra equipped with a positive state and its Gelfand–Naimark–Segal (GNS) representation. The central construction is a projected fusion product on normalized quadratic current operators. Within the closed current sector, $P_{\rm rel}(O_A^2)=2O_A$ up to irrelevant corrections, and ultraviolet self-similarity expressed as $X_A\star X_A=X_A$ with $X_A=r_AO_A$ yields the interacting normalized fixed point $r_A^*=1/2$. With the retained operator basis fixed by the GNS Gram metric, a reduced per-generation fermionic current convention for the gauge sectors and canonical graviton normalization give a common algebraic value for $(10/3)g_Y^2$, $2g_2^2$, $2g_3^2$, and $32\pi G\mu^2$. We discuss conditional emergence of Lorentzian geometry and Einstein gravity, a Standard-Model-like internal algebra, three generation channels from a minimal quartic pairing sector, minimal selection of a $3+1$ dimensional branch, and relational time with a branch-dependent arrow of records. A Standard Model–Pati–Salam renormalization-group analysis provides a phenomenological consistency test of the proposed ultraviolet basin.

Motivated by the fact that quantum effects leave an imprint on the vacuum equation of state, making it depart from the standard cosmological constant relation, $P_{\rm vac}=-\rho_{\rm vac}$, this work investigates generalized running vacuum models (RVMs) by considering a dynamical vacuum equation of state in which the vacuum energy density, $\rho_{\text{vac}}$, evolves as a function of the Hubble parameter, $H$, and its time derivative, $\dot{H}$. This formulation extends previous running vacuum approaches by incorporating a dependence of the vacuum energy density on both, $H^2$ and $\dot{H}$. The corresponding Friedmann equations are derived and analyzed to study their impact on cosmic expansion. The model parameters are constrained through a joint statistical analysis combining the cosmic microwave background shift parameters, DESI-DR2 observations, PantheonPlus type Ia supernovae compilation, and Hubble rate $H(z)$ measurements. Model comparison is performed using information criteria, the Akaike Information Criterion (AIC) and Deviance Information Criterion (DIC), in order to assess the statistical performance of the RVMs relative to the standard $\Lambda$CDM scenario. The results show that the generalized RVMs provide a good fit to current observations and represent a statistically competitive alternative to the standard $\Lambda$CDM model. Notably, all three running vacuum formulations yield lower AIC and DIC values than $\Lambda$CDM, indicating that dynamical running vacuum energy remains a viable cosmological scenario.

The next-generation pressure standard is moving toward optical-based, field-deployable systems. However, most existing optical refractometry pressure standards rely on bulky ultra-low expansion (ULE) cavities and complex feedback locking, limiting their portability and on-site applicability. Here, we present a miniaturized, transportable optical pressure manometer based on a dual-channel Fabry-Perot cavity machined from a single block of common fused silica. By employing a differential measurement between an evacuated reference cavity and a gas-exposed measurement cavity, common-mode errors such as thermal expansion and pressure-induced deformation are largely canceled, enabling the use of low-cost fused silica to achieve performance comparable to ULE. Radio-frequency scanning with Lorentzian fitting replaces conventional feedback locking, simplifying the optical design and improving robustness. Calibrated against a piston manometer, the device demonstrates a measurement repeatability of 3.4~ppm and a total uncertainty of \(u = \sqrt{(10.6\times10^{-6}p)^2 + (5.4~\mathrm{mPa})^2}\). The system can resolve periodic pressure fluctuations originating from the piston manometer and exhibits superior response speed. With its small footprint, portability, and independence from external frequency references, this fused-silica dual-cavity manometer offers a practical route toward on-site, quantum-traceable pressure calibration.

Accurate system-level prediction of cryogenic liquid storage remains challenging because reduced-order models rely on regime-dependent closures for unresolved heat and mass transfer, particularly under sloshing. We present a physics-integrated neural-network framework that combines a conservation-based zero-dimensional nodal model with data-driven closures for wall and interfacial heat transfer, phase change, pressurant quality, and liquid thermal-boundary-layer evolution. Thermal stratification and mixing within the liquid are represented through a first-order dynamical model for the boundary-layer thickness, while four operating-regime-specific neural networks infer the closure parameters for self-pressurization and relaxation, active pressurization, venting, and lateral sloshing. The framework was identified and evaluated using a dedicated database of 48 multi-stage cryogenic-tank experiments conducted in an optically accessible facility operated with liquid nitrogen. The experiments combine controlled wall heating, vapor injection and evacuation, and forced lateral sloshing, thereby covering both slowly evolving thermal states and strongly transient operating conditions. Generalization was assessed through experiment-level K-fold cross-validation, while an entropy-production penalty was included in the loss function to discourage violations of the second law of thermodynamics. Across the investigated cross-validation configurations, the global normalized root-mean-square error remained under 3%, with sloshing representing the most demanding regime. A final model trained on the complete database reconstructed the experiments with a global error of 1.6%. These results demonstrate that the proposed framework can extract physically interpretable and computationally efficient closure laws from a limited but information-rich experimental database.

Since the discovery of the Higgs particle in the LHC, numerous inflationary models utilize it as the inflaton. In this study, after establishing that Higgs inflation can be a viable model in the context of unimodular gravity, we address a scenario related to reheating, which plays a crucial role in connecting the inflationary era to a hot Big Bang universe. Also, we calculate essential parameters such as the temperature and the e-folds number according to the equation of the state parameter ($\omega_{re}$) in this regime of reheating. The physics behind the reheating process are extremely imprecise at present, and we have only a very limited range of acceptable values for $\omega_{re}$. We analyze the compatibility with Planck2018, BICEP/Keck2021, DESI2024, and ACT array bounds and find that within this model, $\omega_{re}$ is restricted to the range $ -1 \leq \omega_{re} \leq \frac{1}{6} $.

We investigate the observational viability of the linear Herglotz-type $f(R,T)$ gravity model, $f(R,T)=R+\alpha T$, which incorporates both geometry–matter coupling and non-conservative gravitational dynamics. Unlike previous analyses\cite{Wazny:2025jth} based on illustrative parameter choices, we perform a systematic Bayesian estimation of the four-dimensional parameter space $\{H_0,A,w,\Phi_0\}$, where $A$ characterizes the matter–geometry coupling, $w$ is the effective equation-of-state parameter, and $\Phi_0$ denotes the present-day Herglotz field. The background evolution is obtained by numerically integrating the coupled Herglotz cosmological equations at every point in the parameter space. We employ Cosmic Chronometer (CC), DESI DR2 baryon acoustic oscillation (BAO), and Union3 Type-Ia supernova data, both independently and in combination. The joint analysis yields $H_0=66.67^{+1.32}_{-1.28}\,\mathrm{km\,s^{-1}\,Mpc^{-1}}$, $A=1.57^{+0.66}_{-0.51}$, $w=-0.992^{+0.136}_{-0.119}$, and $\Phi_0=-0.062^{+0.185}_{-0.157}$ at $68\%$ credibility. The reconstructed Hubble expansion closely follows the flat $\Lambda$CDM prediction over the redshift range probed by the CC data. However, the deceleration parameter, effective equation of state, $Om(z)$ diagnostic, and statefinder $\{r,s\}$ trajectories exhibit appreciable departures from the concordance model, with the magnitude and redshift evolution depending on the observational dataset. These results demonstrate that Herglotz-type $f(R,T)$ gravity can provide an observationally viable description of the late-time expansion while retaining distinguishable cosmological signatures beyond the background Hubble history.

We review recent calculations and numerical simulations showing the formation of coherent states of protons in hydrogen-loaded metals with a cubic crystal lattice. In these states protons oscillate coherently at frequencies of the order of $10^{13}\,\mathrm{Hz}$ and in a fixed phase relation with a strong high-frequency electric field which is trapped in the material, especially if the material is made of micro-powders. The energy gap of the coherent ground state is estimated to be well above thermal energies, of the order of a fraction of an eV per particle, and therefore large enough to make the state robust against thermal fluctuations. The analytical calculations address the realistic case of a large number of protons, in the rotating-wave approximation. The numerical calculations are presently limited to a small number of protons but go beyond the rotating-wave approximation and allow one to take into account a dissipation term associated with the strong oscillating electric field. The next task of this theoretical model is to compute the excited states of the coherent system. There are strong indications that in those states protons can be excited by an external pump to energies much larger than those achievable by single incoherent protons in condensed matter. Such energies are large enough to make possible some electron-capture processes, with generation of slow neutrons. This dynamical mechanism offers an alternative to the Widom–Larsen hypothesis of “heavy electrons”, and is closer to current models in mainstream physics. The consequences, in terms of nuclear transmutations, of neutron generation via electron capture would be similar to those predicted by Widom and Larsen, plus several other processes like those recently re-examined by Metzler et al.

We report cryogenic characterization and compact modeling of GlobalFoundries (GF) 12LP regular-voltage-threshold (RVT) n- and p-FinFETs, measured from 292 K to 10 mK. Both devices retain sub-Kelvin gate control without carrier freeze-out, with the n-type device exhibiting an intrinsic sub-threshold slope (SS) floor of 24.8 mV/dec. To bypass high on-chip series routing resistance that confounds peak-gm extraction, we adopt a fixed-current (3.26 uA/um) methodology. These low-current metrics inform a continuous 1.36 K to 292 K compact model using dynamic parameter injection, preserving room-temperature process development kit (PDK) qualification.

We construct regular, horizon-admitting compact objects supported entirely by a self-gravitating dark-matter fluid, in the one-parameter curvature-gravity family $f(R)=R+\beta R^n$. Working with the Einasto density profile, we derive the anisotropic fluid field equations for a static, spherically symmetric metric and obtain the exact General Relativity limit under a de~Sitter-type equation of state, in which the central singularity is replaced by a regular de~Sitter core and the solution is either a horizonless droplet or a black hole with one or two Killing horizons, depending on a single rescaled-mass parameter. We compute the resulting Hawking temperature and geodesic effective potential, and – exploiting the linearity of the $\beta=0$ field equation – solve the curvature correction perturbatively in closed form for general $n$, showing that its sign and radial shape are genuinely model-dependent by direct comparison at fixed $\beta$ between $n=2$ (Starobinsky) and $n=3$ (cubic) gravity. We repeat the construction for a non-local equation of state and confirm the resulting droplets are curvature-regular via the Kretschmann scalar. Finally, replacing the Einasto profile with the cored Burkert profile preserves the qualitative regularity mechanism but, because the Burkert halo lacks a finite total mass, produces a horizon structure with inner and outer radii separated by nearly three orders of magnitude – a genuine physical distinction between two comparably realistic dark-matter models.

In this study, we use the harmonic oscillator s energy spectrum to connect its dynamical behavior to the formalism of statistical mechanics through entropy. We perform a thermal analysis of the entropy generated by this spectrum in both commutative and noncommutative two-dimensional configuration spaces, employing the Tsallis and Renyi entropy measures. The primary objective is to examine the possibility of an intrinsic link and mutual influence between the noncommutative parameter({\theta}) and the parameters arising from generalized entropies. By analyzing both Tsallis and Renyi frameworks, we investigate whether a fundamental relationship exists between {\theta} and the entropy index q. Establishing such a connection could provide new insights into the interplay between spacetime geometry and generalized statistical mechanics.

In the framework of $f(Q)$ gravity, we investigate whether spatial curvature can be made dynamically invisible in the cosmological background equations. We consider open spatial sections, $k<0$, on an explicitly specified homogeneous and isotropic symmetric-teleparallel connection branch. For $k\neq0$, the coincident gauge cannot be imposed simultaneously with the standard curved-FLRW coordinate form. Re-deriving the background equations from the minisuperspace action, we show that curvature enters through $x=H+\delta\sqrt{-k}/a$ and appears with inequivalent weights in the energy and pressure equations. For $f\in C^3((0,\infty))$, we prove a branch-specific no-go theorem: strict curvature independence for every scale factor and every $k<0$ requires $f=\mathrm{const}$, which contains no metric kinetic term. STEGR is not curvature-neutral, since its Friedmann equation retains the usual $3k/a^2$ contribution. A weaker cancellation, imposed only on backgrounds satisfying $\delta\sqrt{-k}/a=cH$, necessarily produces a coasting expansion and yields $f(Q)=A Q^{(c+2)/2}+B$, or $f(Q)=A\ln Q+B$ when $c=-2$. For the illustrative choice $c=-3$, the solution becomes $f=\alpha_1/\sqrt Q+\beta_1$. Under the conventional positive-coupling assumption $f_Q>0$, the required source violates the null energy condition. Moreover, adding positive radiation or pressureless matter forces a compensating negative-energy component at sufficiently early times. The weak branch is therefore neither curvature-neutral in an invariant sense nor a viable cosmological model. The principal result is the background-level obstruction itself. Perturbative stability and gravitational-wave propagation require a separate analysis including perturbations of the nontrivial affine connection and are not established in this work.

We study the cosmological features of Rastall gravity, where the covariant energy-momentum conservation is modified to $\nabla_{\mu}T^{\mu}_{\nu}=\lambda \nabla_{\nu}R$ in curved spacetime. For this purpose, we obtain the modified field equations of Rastall model to linear order of perturbations, and then inspect the evolutionary behavior of cosmological observables, chiefly the matter power spectrum and the Hubble parameter, within the context of Rastall gravity. We also compare Rastall model with cosmological probes, namely cosmic microwave background, weak lensing, supernovae, baryon acoustic oscillations, and redshift-space distortions data. According to our numerical results, Rastall gravity prefers lower growth of structures compared to the $\Lambda$CDM model, which indicates consistency with low-redshift large-scale structure probes. Moreover, numerical analysis reveals that Rastall gravity with a cosmological constant as the dark energy component suffers from the Hubble tension, like the $\Lambda$CDM model.

Performance claims in quantum technology are not properties of hardware alone. They are properties of a declared task, system boundary, normalization denominator, uncertainty or security convention, and comparator. We perform a cross-domain analysis spanning quantum computing, simulation, communication, sensing, clocks, randomness generation, and their enabling technologies. The analysis changes substantive conclusions in several representative cases. For the longest direct finite-key quantum key distribution case analyzed here, the same final key gives rates differing by a factor of $1.91$ when normalized by complete acquisition rather than transmission-active time. In Advanced LIGO, $6.1\,\mathrm{dB}$ peak quantum-noise reduction coexists with a $0.534$ coincident analysis-ready fraction, separating detector-level gain from delivered observing service. In quantum computation and photonic sampling, matching the observable, error tolerance, loss model, sample count, amortization, and classical hardware moves or reverses published crossover claims. Across domains, the recurring limits are correlated error, multiplicative interface loss, thermal and nonequilibrium occupation, calibration covariance, measurement efficiency, fabrication yield, and control latency. A quantum advantage is therefore established only for a fixed task and boundary when the accepted output outperforms the best documented alternative at matched accuracy, elapsed time, availability, and lifecycle cost. The resulting framework identifies the measurements required to convert component records into reproducible system capability. Credible progress is defined by reproduced logical workloads, prospectively validated simulations, repeater links outperforming direct transmission, long-duration calibrated sensors and clocks, integrated hardware with predictable yield and reliability.

We investigate the cosmological evolution of a flat Friedmann–Robertson–Walker Universe filled with Tsallis holographic dark energy (THDE) under the assumption that the gravitational constant $G$ varies with time according to the power-law parametrisation $d\ln G / d\ln a = \alpha_G = \mathrm{const}$. In this framework, the holographic dark energy density is given by $\rho_{\mathrm{DE}} \propto L^{2\gamma - 4}$, where $L$ is the future event horizon and $\gamma$ is the Tsallis non-additivity parameter. We study both the past and future evolution of the Universe for various values of the model parameters $C$, $\gamma$, and $\alpha_G$. The viability of the model is tested against a combination of observational data, including the Pantheon+ Type Ia supernova sample, direct Hubble parameter measurements $H(z)$, and baryon acoustic oscillation (BAO) data. Using Markov Chain Monte Carlo (MCMC) methods and Bayesian analysis tools such as the Deviance Information Criterion (DIC), the Bayes factor, and the suspiciousness metric, we perform a rigorous statistical comparison with the standard $\Lambda$CDM model. Our results show that models with a varying gravitational constant are preferred over $\Lambda$CDM. The best fit to the combined data is obtained for the THDE model with $C < 1$. Furthermore, we analyse the internal consistency of the data sets using the Index of Inconsistency, the $Q_{\mathrm{DMAP}}$ statistic, and Bayesian suspiciousness. We find that the THDE model with varying $G$ and $C < 1$ partially alleviates the tensions between different probes, reducing the significance from $\sim 7.4\sigma$ to $\sim 5.3\sigma$.

Strong lensing around a rotating black hole produces delayed and rotated higher-order images even in Kerr. We ask how a dark matter (DM) environment changes these photon-ring echoes after the leading ring scale is matched to Kerr. We follow the signal from rotating DM geometry to finite-order photon transfer, slow-light emission, interferometric visibilities, and source-population tests. For a strong central-spike benchmark with $a/M=0.8$ and $i=70^\circ$, a $1.49\%$ critical-parameter fingerprint remains after ring matching. The order-1 and order-2 delay medians are $13.33M$ and $33.06M$, and the 230-GHz static and dynamic visibility contrasts are $0.070F_0$ and $0.112F_0$. The differential signal also remains distinct in a shared-source oracle test. The harder step is attribution when the source is unknown. Raw EHT-like closures give AUC $0.658$, while fresh validation with total-flux and compact spatial source drivers gives $0.507$ and $0.500$. We therefore use the loss of separation on new sources to derive observing requirements rather than a detection claim. At the pre-defined Kerr threshold, 75% power requires $d=2.319$, compared with $d=0.553$ for the raw independent-source test. Under a fixed-mean diagnostic, the residual source scatter would need to be about $0.238$ of its present value, although the bootstrap range $0.022$–$0.444$ is broad. Daily gaps can also miss the smaller spike–Kerr delay difference. Finding a photon echo and attributing a small deformation to DM are therefore different tasks. Robust attribution needs source control and suitable delay coverage, not sensitivity alone.

In this paper, we study linear perturbations of a geometrically regular black hole supported by a constrained $\mathrm{SO}(3)$ scalar triplet in the hedgehog configuration. Since the individual background scalars depend explicitly on the angular coordinates, the decoupling of polar and axial perturbations cannot be concluded from the spherical form of the metric or the energy–momentum tensor alone. To settle this point, we introduce the polar and axial metric and triplet amplitudes simultaneously and derive the corresponding projections of the radiative linearized Einstein–matter equations for $\ell\geq2$. The polar equations contain only polar amplitudes, whereas the axial equations contain only axial amplitudes; hence, the two off-diagonal blocks vanish at linear order. The resulting odd-parity sector forms a closed Einstein–scalar system in which a tangent perturbation of the scalar triplet is coupled to the Regge–Wheeler metric amplitudes. We show that its scalar equation has a second-order hyperbolic principal part whenever $K_Y\neq0$, and that, for the nonlinear kinetic function supporting the background, $K_Y>0$ throughout the black-hole exterior. The coefficient of the direct metric–scalar mixing is largest at the event horizon and decreases as $r^{-4}$ at large distance, while the metric block in the vacuum limit reproduces the standard Regge–Wheeler equation and potential; the scalar kinetic coefficient simultaneously vanishes, so the full operator changes rank. These results establish linear parity decoupling and the consistency of the closed axial equations. They do not, however, constitute a proof of mode stability, which requires the reduction of the complete quadratic action.

Barrow holographic dark energy connects cosmic acceleration with possible quantum-gravitational deformations of horizon entropy, encoded in the Barrow exponent $\Delta$. If such effects are scale dependent, however, there is no fundamental reason for $\Delta$ to remain constant throughout cosmic history. In this work we reconstruct $\Delta(z)$ directly from observations, without assuming any particular functional form, using the Cosmo-PINN physics-informed neural-network framework. The generalized Barrow holographic evolution equation is incorporated into the training, while PantheonPlus supernovae, DESI DR2 baryon acoustic oscillations and cosmic chronometers constrain the reconstruction. We find a mild and smooth redshift evolution, with the posterior mean favoring negative $\Delta$ and this tendency becoming stronger when the Cepheid calibration is included. Nevertheless, $\Delta=0$ and constant negative values remain compatible with current uncertainties. The reconstructed cosmology yields a viable late-time evolution, with $w_{\rm DE}$ close to $-1$ and the expected transition to accelerated expansion. Our results demonstrate that cosmological observations can directly probe the functional behavior of a quantity entering the underlying entropy law itself.

Spectrally stable cascades can undergo enormous transient growth before eventually dying out. We show that this amplification is controlled by the directed architecture of the interactions, independently of the eigenvalues that determine asymptotic stability. More remarkably, when several critical subsystems are connected sequentially, their depth becomes a new control parameter for critical fluctuations: each additional critical stage generates a new cascade-size exponent, producing an infinite hierarchy of universality classes. This result follows because the fluctuating population produced at one stage becomes the random input to the next. The mechanism persists for both finite-variance and heavy-tailed reproduction and strongly enhances the probability of rare terminal events. Applied to multitype earthquake triggering, it provides a stationary mechanism for the anomalously large abundance of foreshock-mainshock sequences. Directed architecture can therefore control both transient amplification and critical statistics in cascade processes even when it leaves spectral stability unchanged.