Anisotropic Generalized Ghost Pilgrim Dark Energy Model in General Relativity

A spatially homogeneous and anisotropic locally rotationally symmetric (LRS) Bianchi type-I Universe filled with matter and generalized ghost pilgrim dark energy (GGPDE) has been studied in general theory of relativity. To obtain determinate solution of the field equations we have used scalar expansion proportional to the shear scalar which leads to a relation between the metric potentials. Some well-known cosmological parameters (equation of state (EoS) parameter (ω _Λ), deceleration parameter (q) and squared speed of sound \({v_{s}^{2}}\)) and planes (\(\omega _{\Lambda }-\dot {\omega }_{\Lambda }\) and statefinder) are constructed for obtained model. The discussion and significance of these parameters is totally done through pilgrim dark energy parameter (β) and cosmic time (t).     

Interacting Generalized Ghost Dark Energy in Non-isotropic Background

In this work, the generalized Quantum Chromodynamics (QCD) ghost model of dark energy in the framework of Einstein gravity is investigated. At first, the non-interacting generalized ghost dark energy in a Bianchi type I (BI) background is discussed. Then the equation of state parameter, ω _D = p _D /ρ _D , the deceleration parameter, and the evolution equation of the generalized ghost dark energy are obtained. It was found that, in this case, ω _D cannot cross the phantom line (ω _D >?1) and eventually the universe approaches a de-Sitter phase of expansion (ω _D →?1). Then, this investigation was extended to the interacting ghost dark energy in a non-isotropic universe. It was found that the equation of state parameter of the interacting generalized ghost dark energy can cross the phantom line (ω _D <?1) provided the parameters of the model are chosen suitably. It was considered a specific model which permits the standard continuity equation in this theory. Besides Ω_Λ and Ω _m in standard Einstein cosmology, another density parameter, Ω _σ , is expected by the anisotropy. The anisotropy of the universe decreases and the universe transits to an isotropic flat FRW universe accommodating the present acceleration.     

Cosmological analysis of reconstructed $${\mathcal {F}}(T,T_{\mathcal {G}})$$ models

In this paper, we analyze cosmological consequences of the reconstructed generalized ghost pilgrim dark energy \({\mathcal {F}}(T,T_{\mathcal {G}})\) models in terms of redshift parameter z. For this purpose, we consider power-law scale factor, scale factor for two unified phases and intermediate scale factor. We discuss graphical behavior of the reconstructed models and examine their stability analysis. Also, we explore the behavior of equation of state as well as deceleration parameters and \(\omega _{\Lambda }-\omega _{\Lambda }^{'}\) as well as \(r-s\) planes. It is found that all models are stable for pilgrim dark energy parameter 2. The equation of state parameter satisfies the necessary condition for pilgrim dark energy phenomenon for all scale factors. All other cosmological parameters show great consistency with the current behavior of the universe.     

Ghost Dark Energy with Non-Linear Interaction Term

Here we investigate ghost dark energy (GDE) in the presence of a non-linear interaction term between dark matter and dark energy. To this end we take into account a general form for the interaction term. Then we discuss about different features of three choices of the non-linear interacting GDE. In all cases we obtain equation of state parameter, w _D = p/ρ, the deceleration parameter and evolution equation of the dark energy density parameter (Ω _D ). We find that in one case, w _D cross the phantom line (w _D < ?1). However in two other classes w _D can not cross the phantom divide. The coincidence problem can be solved in these models completely and there exist good agreement between the models and observational values of w _D , q. We study squared sound speed \({v_{s}^{2}}\), and find that for one case of non-linear interaction term \({v_{s}^{2}}\) can achieves positive values at late time of evolution.     

A Study of Holographic Dark Energy Models in Chern-Simon Modified Gravity

This paper is devoted to study some holographic dark energy models in the context of Chern-Simon modified gravity by considering FRW universe. We analyze the equation of state parameter using Granda and Oliveros infrared cut-off proposal which describes the accelerated expansion of the universe under the restrictions on the parameter α. It is shown that for the accelerated expansion phase \( -1<\omega _{\Lambda }<-\frac {1}{3}\), the parameter α varies according as \(1<\alpha <\frac {3}{2}\). Furthermore, for 0<α<1, the holographic energy and pressure density illustrates phantom-like theory of the evolution when ω_Λ<?1. Also, we discuss the correspondence between the quintessence, K-essence, tachyon and dilaton field models and holographic dark energy models on similar fashion. To discuss the accelerated expansion of the universe, we explore the potential and the dynamics of quintessence, K-essence, tachyon and dilaton field models.     

A New Set of Limiting Gibbs Measures for the Ising Model on a Cayley Tree

For the Ising model (with interaction constant J>0) on the Cayley tree of order k≥2 it is known that for the temperature T≥T _c,k =J/arctan?(1/k) the limiting Gibbs measure is unique, and for T<T _c,k there are uncountably many extreme Gibbs measures. In the Letter we show that if \(T\in(T_{c,\sqrt{k}}, T_{c,k_{0}})\), with \(\sqrt{k} then there is a new uncountable set \({\mathcal{G}}_{k,k_{0}}\) of Gibbs measures. Moreover \({\mathcal{G}}_{k,k_{0}}\ne {\mathcal{G}}_{k,k'_{0}}\), for k ₀≠k′₀. Therefore if \(T\in (T_{c,\sqrt{k}}, T_{c,\sqrt{k}+1})\), \(T_{c,\sqrt{k}+1} then the set of limiting Gibbs measures of the Ising model contains the set {known Gibbs measures}\(\cup(\bigcup_{k_{0}:\sqrt{k}.     

<Emphasis Type="Italic">U</Emphasis>(2) and minimal flavour violation in supersymmetry

Rather than sticking to the full U(3)³ approximate symmetry normally invoked in Minimal Flavour Violation, we analyze the consequences on the current flavour data of a suitably broken U(2)³ symmetry acting on the first two generations of quarks and squarks. A definite correlation emerges between the ΔF=2 amplitudes \(\mathcal{M}( K^{0} \to \bar{K}^{0} )\), \(\mathcal{M}( B_{d} \to \bar{B}_{d} )\) and \(\mathcal{M}( B_{s} \to \bar{B}_{s} )\), which can resolve the current tension between \(\mathcal{M}( K^{0} \to \bar{K}^{0} )\) and \(\mathcal{M}( B_{d} \to \bar{B}_{d} )\), while predicting \(\mathcal{M}( B_{s}\to \bar{B}_{s} )\). In particular, the CP violating asymmetry in B _s →ψφ is predicted to be positive S _ψφ =0.12±0.05 and above its Standard Model value (S _ψφ =0.041±0.002). The preferred region for the gluino and the left-handed sbottom masses is below about 1÷1.5 TeV. An existence proof of a dynamical model realizing the U(2)³ picture is outlined.     

Vector tetraquark state candidates: <Emphasis Type="Italic">Y</Emphasis>(4260 / 4220), <Emphasis Type="Italic">Y</Emphasis>(4360 / 4320), <Emphasis Type="Italic">Y</Emphasis>(4390) and <Emphasis Type="Italic">Y</Emphasis>(4660 / 4630)

In this article, we construct the \(C \otimes \gamma _\mu C\) and \(C\gamma _5 \otimes \gamma _5\gamma _\mu C\) type currents to interpolate the vector tetraquark states, then carry out the operator product expansion up to the vacuum condensates of dimension-10 in a consistent way, and obtain four QCD sum rules. In calculations, we use the formula \(\mu =\sqrt{M^2_{Y}-(2{\mathbb {M}}_c)^2}\) to determine the optimal energy scales of the QCD spectral densities, moreover, we take the experimental values of the masses of the Y(4260 / 4220), Y(4360 / 4320), Y(4390) and Y(4660 / 4630) as input parameters and fit the pole residues to reproduce the correlation functions at the QCD side. The numerical results support assigning the Y(4660 / 4630) to be the \(C \otimes \gamma _\mu C\) type vector tetraquark state \(c\bar{c}s\bar{s}\), assigning the Y(4360 / 4320) to be \(C\gamma _5 \otimes \gamma _5\gamma _\mu C\) type vector tetraquark state \(c\bar{c}q\bar{q}\), and disfavor assigning the Y(4260 / 4220) and Y(4390) to be the pure vector tetraquark states.     

Hypersurfaces Satisfying <Emphasis Type="BoldItalic">τ</Emphasis><Subscript><Emphasis Type="BoldItalic">2</Emphasis></Subscript><Emphasis Type="BoldItalic">(ϕ) = ητ(ϕ)</Emphasis> in Pseudo-Riemannian Space Forms

In this paper, we derived the equations for the hypersurface \({M^{n}_{r}}\) of a pseudo-Riemannian space form \(N^{n+1}_{q}(c)\) to satisfy τ ₂(?) = η τ(?) (η a constant) with τ(?) and τ ₂(?) be the tension and bitension fields of \({M^{n}_{r}}\). As applications, we prove that a hypersurface \({M^{n}_{r}}\) satisfying τ ₂(?) = η τ(?) in \(N^{n+1}_{q}(c)\) has constant mean curvature, under the assumption that \({M^{n}_{r}}\) has diagonalizable shape operator with at most three distinct principal curvatures. Then, using this result, we classify partially such hypersurface. We also make a preliminary study of hypersurfaces satisfying τ ₂(?) = f τ(?) with f be function.     

A parametric reconstruction of the deceleration parameter

The present work is based on a parametric reconstruction of the deceleration parameter q(z) in a model for the spatially flat FRW universe filled with dark energy and non-relativistic matter. In cosmology, the parametric reconstruction technique deals with an attempt to build up a model by choosing some specific evolution scenario for a cosmological parameter and then estimate the values of the parameters with the help of different observational datasets. In this paper, we have proposed a logarithmic parametrization of q(z) to probe the evolution history of the universe. Using the type Ia supernova, baryon acoustic oscillation and the cosmic microwave background datasets, the constraints on the arbitrary model parameters \(q_{0}\) and \(q_{1}\) are obtained (within \(1\sigma \) and \(2\sigma \) confidence limits) by \(\chi ^{2}\)-minimization technique. We have then reconstructed the deceleration parameter, the total EoS parameter \(\omega _\mathrm{tot}\), the jerk parameter and have compared the reconstructed results of q(z) with other well-known parametrizations of q(z). We have also shown that two model selection criteria (namely, the Akaike information criterion and Bayesian information criterion) provide a clear indication that our reconstructed model is well consistent with other popular models.     

Method of uniform effective field in structure-dynamic approach of nanoionics

In the structure-dynamic approach of nanoionics, the method of a uniform effective field \( {F}_{\mathrm{eff}}^{j,k} \) of a crystallographic planeX ^j has been substantiated for solid electrolyte nanostructures. The \( {F}_{\mathrm{eff}}^{j,k} \)is defined as an approximation of a non-uniform field \( {F}_{\mathrm{dis}}^j \)of X ^j with a discrete- random distribution of excess point charges. The parameters of \( {F}_{\mathrm{eff}}^{j,k} \)are calculated by correction of the uniform Gauss field \( {F}_{\mathrm{G}}^j \) of X ^j . The change in an average frequency of ionic jumps X ^k ?→?X ^k?+?1 between adjacent planes of nanostructure is determined by the sum of field additives to the barrier heights η _k , _k?+?1, and for \( {F}_{\mathrm{G}}^j \) and \( {F}_{\mathrm{dis}}^j \), these sums are the same decimal order of magnitude. For nanostructures with length ~4 nm, the application of \( {F}_{\mathrm{G}}^j \) (as \( {F}_{\mathrm{eff}}^{j,k} \)) gives the accuracy ~20 % in calculations of ion transport characteristics. The computer explorations of the “universal” dynamic response (Reσ ^??∝?ω ⁿ ) show an approximately the same power n < ≈1 for\( {F}_{\mathrm{G}}^j \) and \( {F}_{\mathrm{eff}}^{j,k} \).     

Parabolic Presentations of the Super Yangian {Y(\mathfrak{gl}_{M|N})} Associated with Arbitrary 01-Sequences

Let μ be an arbitrary composition of M + N and let \({\mathfrak{s}}\) be an arbitrary \({0^{M}1^{N}}\)- sequence. A new presentation, depending on \({\mu \rm and \mathfrak{s}}\), of the super Yangian Y_M|N associated to the general linear Lie superalgebra \({\mathfrak{gl}_{M|N}}\) is obtained.     

A Note on Holographic Dark Energy with Varying <Emphasis Type="Italic">c</Emphasis><Superscript>2</Superscript> Term

We reconsider the holographic dark energy (HDE) model with a slowly time varying c ²(z) parameter in the energy density, namely \(\rho _{D}=3{M_{p}^{2}} c^{2}(z)/L^{2}\), where L is the IR cutoff and z is the redshift parameter. As the system’s IR cutoff we choose the Hubble radius and the Granda-Oliveros (GO) cutoffs. The latter inspired by the Ricci scalar curvature. We derive the evolution of the cosmological parameters such as the equation of state and the deceleration parameters as the explicit functions of the redshift parameter z. Then, we plot the evolutions of these cosmological parameters in terms of the redshift parameter during the history of the universe. Interestingly enough, we observe that by choosing L = H ^?1 as the IR cutoff for the HDE with time varying c ²(z) term, the present acceleration of the universe expansion can be achieved, even in the absence of interaction between dark energy and dark matter. This is in contrast to the usual HDE model with constant c ² term, which leads to a wrong equation of state, namely that for dust w _D =0, when the IR cutoff is chosen the Hubble radius.     

Collision Index and Stability of Elliptic Relative Equilibria in Planar {n}-body Problem

In this article, we construct three new holomorphic vertex operator algebras of central charge 24 using the \({\mathbb{Z}_{2}}\)-orbifold construction associated to inner automorphisms. Their weight one subspaces have the Lie algebra structures D_7,3A_3,1G_2,1, E_7,3A_5,1, and \({A_{8,3}A_{2,1}^2}\). In addition, we discuss the constructions of holomorphic vertex operator algebras with Lie algebras A_5,6C_2,3A_1,2 and \({D_{6,5}A_{1,1}^2}\) from holomorphic vertex operator algebras with Lie algebras C_5,3G_2,2A_1,1 and \({A_{4,5}^2}\), respectively.     

Phantom divide crossing with general non-minimal kinetic coupling

We propose a model of dark energy consists of a single scalar field with a general non-minimal kinetic couplings to itself and to the curvature. We study the cosmological dynamics of the equation of state in this setup. The coupling terms have the form \({\xi_{1} Rf(\phi)\partial_{\mu}\phi\partial^{\mu}\phi}\) and \({\xi_{2}R_{\mu\nu}f(\phi)\partial^{\mu}\phi\partial^{\nu}\phi}\) where ξ ₁ and ξ ₂ are coupling parameters and their dimensions depend on the type of function \({f(\phi)}\). We obtain the conditions required for phantom divide crossing and show numerically that a cosmological model with general non-minimal derivative coupling to the scalar and Ricci curvatures can realize such a crossing.     

Applications of the Stroboscopic Tomography to Selected 2-Level Decoherence Models

In the paper we discuss possible applications of the so-called stroboscopic tomography (stroboscopic observability) to selected decoherence models of 2-level quantum systems. The main assumption behind our reasoning claims that the time evolution of the analyzed system is given by a master equation of the form \(\dot {\rho } = \mathbb {L} \rho \) and the macroscopic information about the system is provided by the mean values m _i (t _j ) = T r(Q _i ρ(t _j )) of certain observables \(\{Q_{i}\}_{i=1}^{r} \) measured at different time instants \(\{t_{j}\}_{j=1}^{p}\). The goal of the stroboscopic tomography is to establish the optimal criteria for observability of a quantum system, i.e. minimal value of r and p as well as the properties of the observables \(\{Q_{i}\}_{i=1}^{r} \).     

On a Pre-Lie Algebra Defined by Insertion of Rooted Trees

Let K be a field of characteristic zero. For \({n \in \mathbb{N}^{*}}\) , let \({\mathcal{T}^{\,\prime}_{n}}\) be the vector space of non-planar rooted trees with n vertices (Foissy in Bull Sci Math 126, no. 3, 193–239; no. 4, 249–288, 2002). Let \({\vartriangleright}\) be the left pre-Lie product of insertion of a tree inside another defined on infinitesimal characters of the graded Hopf algebra \({\mathcal{H}}\) introduced by Calaque, Ebrahimi-Fard and Manchon. Let \({\mathcal{T}^{\,\prime}=\oplus_{n\geq 2}\mathcal{T}^{\,\prime}_{n}}\) . In this work, we first prove that \({(\mathcal{T}^{\,\prime}, \vartriangleright)}\) a pre-Lie algebra generated by the two ladders E ₁ and E ₂ where E ₁ is the ladder with one edge and E ₂ is the ladder with two edges. Second, we prove that \({(\mathcal{T}^{\,\prime}, \vartriangleright)}\) is not a free pre-Lie algebra, and we exhibit a family of relations.     

Interference of Nonstandard Interactions with Standard Model in $${B^0} \to {\pi ^0}\bar vv$$, $$B_c^ - \to {D^ - }\bar vv$$Bc−→D−v¯v and $$\bar B_s^0 \to {K^0}\bar vv$$B¯s0→K0v¯v Decays

We study the contributions of nonstandard neutrino interactions (NSI) to the rare decays of pseudoscalar mesons involving neutrinos in the final state \({B^0} \to {\pi ^0}\bar vv\), \(B_c^ - \to {D^ - }\bar vv\) and \(\bar B_s^0 \to {\bar K^0}\bar vv\), It is pointed that dominant contribution comes from the interference between standard model and nonstandard interaction We predict limits on NSIs free parameter ε ^uL _ττ and compare them with experimental data. We further compare our results with perturbative QCD (pQCD) and QCD results for these reactions.     

Asymptotic Behavior of the Selberg Zeta Functions for Degenerating Families of Hyperbolic Manifolds

Let {M _k } be a degenerating sequence of finite volume, hyperbolic manifolds of dimension d, with d = 2 or d = 3, with finite volume limit M _∞. Let \({Z_{M_{k}} (s)}\) be the associated sequence of Selberg zeta functions, and let \({{\mathcal{Z}}_{k} (s)}\) be the product of local factors in the Euler product expansion of \({Z_{M_{k}} (s)}\) corresponding to the pinching geodesics on M _k . The main result in this article is to prove that \({Z_{M_{k}} (s)/{\mathcal{Z}}_{k} (s)}\) converges to \({Z_{M_{\infty}} (s)}\) for all \({s \in \mathbf{C}}\)with Re(s) > (d ? 1)/2. The significant feature of our analysis is that the convergence of \({Z_{M_{k}} (s)/{\mathcal{Z}}_{k} (s)}\) to \({Z_{M_{\infty}} (s)}\) is obtained up to the critical line, including the right half of the critical strip, a region where the Euler product definition of the Selberg zeta function does not converge. In the case d = 2, our result reproves by different means the main theorem in Schulze (J Funct Anal 236:120–160, 2006).