<Emphasis Type="Italic">SU</Emphasis>(2|1) supersymmetric mechanics as a deformation of <Emphasis Type="Italic">N</Emphasis> = 4 mechanics

We give a brief review of SU(2|1) supersymmetric quantum mechanics based on the worldline realizations of the supergroup SU(2|1) in the appropriate N = 4, d = 1 superspaces. The corresponding SU(2|1) models are deformations of standard N = 4, d = 1 models by a mass parameter m.     

Friedmann Cosmology with Matter Creation in Modified <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">R</Emphasis>, <Emphasis Type="Italic">T</Emphasis>) Gravity

The theoretical and observational consequences of thermodynamics of open systems which allow matter creation, are investigated in modified f(R, T) (R is the Ricci scalar and T is the trace of energy-momentum tensor) theory of gravity within the framework of a flat Friedmann-Robertson-Walker line element. The simplest model f(R, T)=R+2f(T) with “gamma-law” equation of state p = (γ?1)ρ is assumed to obtain the exact solution. A power-law expansion model is proposed by considering the natural phenomenological particle creation rate ψ = 3β n H, where β is a pure number of the order of unity, n the particle number density and H is the Hubble parameter. A Big Rip singularity is observed for γ<0 describing phantom cosmology. The accelerated expansion of the Universe is driven by the particle creation. The density parameter shows the negative curvature of the Universe due to particle creation. The entropy increases with the evolution of the Universe. Some kinematics tests such as lookback time, luminosity distance, proper distance, angular diameter versus redshift are discussed in detail to observe the role of particle creation in early and late time evolution of the Universe.     

Bianchi V cosmological model in Palatini <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">R</Emphasis>) gravity

We apply the dynamical systems approach to investigate the spatially homogeneous and anisotropic Bianchi type V models for the Palatini version of f(R) gravity. In particular, we examine the existence of equilibrium points along with their exact solutions and stability properties for two different forms of f(R). Moreover, the evolution of shear and spatial curvature by performing the phase space analysis are studied and also the phases of evolution from anisotropic universe to the stable de-Sitter flat universe are discussed.     

1/<Emphasis Type="Italic">N</Emphasis><Subscript><Emphasis Type="Italic">c</Emphasis></Subscript> countings in baryons

The 1/N _c -power countings for baryon decays and configuration mixings are determined by means of a nonrelativistic quark picture. Such countings are expected to be robust under changes in the quark masses and, therefore, valid as these become light. It is shown that excited baryons have natural widths of \(\mathcal{O}(N_c^0 )\). These dominant widths are due to the decays that proceed directly to the ground-state baryons, with cascade decays being suppressed to \(\mathcal{O}(1/N_c )\). Configuration mixings, defined as mixings between states belonging to different O(3) × SU(2N _f ) multiplets, are shown to be subleading in an expansion in \(1/\sqrt {N_c }\) when they involve the ground-state baryons, while the mixings between excited states can be \(\mathcal{O}(N_c^0 )\).     

Quark diagram analysis of <Emphasis Type="Italic">B</Emphasis>-meson emitting vector (<Emphasis Type="Italic">V</Emphasis>) and vector (<Emphasis Type="Italic">V</Emphasis>) mesons

This paper presents the two body weak nonleptonic decays of B-mesons emitting vector (V) and vector (V) mesons within the framework of the diagrammatic approaches at flavor SU(3) symmetry. We have investigated exclusive two body decays of B-meson using model independent quark diagram scheme. We have shown that the recent measurement of the two body exclusive decays of B-mesons can allow us to determine the magnitude and even sign of the QD amplitude for B → VV decays. Therefore, we become able to make few predictions for their branching fractions.     

Cosmic acceleration in non-flat <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">T</Emphasis>) cosmology

We study f(T) cosmological models inserting a non-vanishing spatial curvature and discuss its consequences on cosmological dynamics. To figure this out, a polynomial f(T) model and a double torsion model are considered. We first analyze those models with cosmic data, employing the recent surveys of Union 2.1, baryonic acoustic oscillation and cosmic microwave background measurements. We then emphasize that the two popular f(T) models enable the crossing of the phantom divide line due to dark torsion. Afterwards, we compute numerical bounds up to 3-\(\sigma \) confidence level, emphasizing the fact that \(\Omega _{k0}\) turns out to be non-compatible with zero at least at 1\(\sigma \). Moreover, we underline that, even increasing the accuracy, one cannot remove the degeneracy between our models and the \(\Lambda \)CDM paradigm. So that, we show that our treatments contain the concordance paradigm and we analyze the equation of state behaviors at different redshift domains. We also take into account gamma ray bursts and we describe the evolution of both the f(T) models with high redshift data. We calibrate the gamma ray burst measurements through small redshift surveys of data and we thus compare the main differences between non-flat and flat f(T) cosmology at different redshift ranges. We finally match the corresponding outcomes with small redshift bounds provided by cosmography. To do so, we analyze the deceleration parameters and their variations, proportional to the jerk term. Even though the two models well fit late-time data, we notice that the polynomial f(T) approach provides an effective de-Sitter phase, whereas the second f(T) framework shows analogous results compared with the \(\Lambda \)CDM predictions.     

The trinification model <Emphasis Type="Italic">SU</Emphasis>(3)<Superscript>3</Superscript> from orbifolds for fuzzy spheres

In this review, we consider an N = 4 supersymmetric SU(3N) gauge theory defined on the Minkowski spacetime. Then we apply an orbifold projection leading to an N = 1 supersymmetric SU(N)³ model, with a truncated particle spectrum. Then, we present the dynamical generation of (twisted) fuzzy spheres as vacuum solutions of the projected field theory, breaking the SU(N)³ spontaneously to a chiral effective theory with unbroken gauge group the trinification group, SU(3)³.     

<Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">R</Emphasis>) gravity constraints from gravitational waves

The recent LIGO observation sparked interest in the field of gravitational wave signals. Besides the gravitational wave observation the LIGO collaboration used the inspiraling black hole pair to constrain the graviton mass. Unlike general relativity, f(R) theories have a characteristic non-zero mass graviton. We apply this constraint on the graviton mass to viable f(R) models in order to find the effects on model parameters. We find it possible to constrain the parameter space with these gravity wave based observations. We consider the popular Hu–Sawicki model as a case study and find an appropriate parameter bracket. The result generalizes to other f(R) theories and can be used to constrain the parameter space.     

Energy conditions in modified <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">G</Emphasis>) gravity

In this paper, we have considered flat Friedmann–Lemaître–Robertson–Walker metric in the framework of perfect fluid models and modified f(G) gravity (where G is the Gauss Bonnet invariant). Particularly, we have considered particular realistic f(G) configurations that could be used to cure finite-time future singularities arising in the late-time cosmic accelerating epochs. We have then developed the viability bounds of these models induced by weak and null energy conditions, by using the recent estimated numerical figures of the deceleration, Hubble, snap and jerk parameters.     

Dark-energy cosmological models in <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">G</Emphasis>) gravity

We discuss dark-energy cosmological models in f(G) gravity. For this purpose, a locally rotationally symmetric Bianchi type I cosmological model is considered. First, exact solutions with a well-known form of the f(G) model are explored. One general solution is discussed using a power-law f(G) gravity model and physical quantities are calculated. In particular, Kasner’s universe is recovered and the corresponding f(G) gravity models are reported. Second, the energy conditions for the model under consideration are discussed using graphical analysis. It is concluded that solutions with f(G) = G^5/6 support expansion of universe while those with f(G) = G^1/2 do not favor the current expansion.     

Extended <Emphasis Type="Italic">E</Emphasis>(5) and <Emphasis Type="Italic">X</Emphasis>(5) symmetries: Series of models providing parameter-independent predictions

The E(5) symmetry describes nuclei related to the U(5)-SO(6) phase transition, while the X(5) symmetry is related to the U(5)-SU(3) phase transition. First, a chain of potentials interpolating between the U(5) symmetry of the five-dimensional harmonic oscillator and the E(5) symmetry is considered. Parameter-independent predictions for the spectra and B(E2) values of nuclei with R₄ = E(4)/E(2) ratios of 2.093, 2.135, and 2.157 (compared to the ratio of 2.000 of the U(5) case and the ratio of 2.199 of the E(5) case) are derived numerically and compared to existing experimental data, suggesting several new experiments. TheX(5) symmetry describes nuclei characterized byR₄=2.904.Using the same separation of variables of the original Bohr Hamiltonian as in X(5), an exactly soluble model with R₄=2.646 is constructed and its parameter-independent predictions are compared to existing spectra and B(E2) values. In addition, a chain of potentials interpolating between this new model and the X(5) symmetry is considered. Parameter-independent predictions for the spectra and B(E2) values of nuclei with R₄ ratios of 2.769, 2.824, and 2.852 are derived numerically and compared to existing experimental data, suggesting several new experiments.     

Quantum Fisher Information for <Emphasis Type="Italic">s</Emphasis><Emphasis Type="Italic">u</Emphasis>(2) Atomic Coherent States and <Emphasis Type="Italic">s</Emphasis><Emphasis Type="Italic">u</Emphasis>(1, 1) Coherent States

We investigate quantum Fisher information (QFI) for s u(2) atomic coherent states and s u(1, 1) coherent states. In this work, we find that for s u(2) atomic coherent states, the QFI with respect to \(\vartheta ~(\mathcal {F}_{\vartheta })\) is independent of φ, the QFI with respect to \(\varphi (\mathcal {F}_{\varphi })\) is governed by ??. Analogously, for s u(1,1) coherent states, \(\mathcal {F}_{\tau }\) is independent of φ, and \(\mathcal {F}_{\varphi }\) is determined by τ. Particularly, our results show that \(\mathcal {F}_{\varphi }\) is symmetric with respect to ?? = π/2 for s u(2) atomic coherent states. And for s u(1,1) coherent states, \(\mathcal {F}_{\varphi }\) also possesses symmetry with respect to τ = 0.     

Exploring plane-symmetric solutions in <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">R</Emphasis>) gravity

The modified theories of gravity, especially the f(R) gravity, have attracted much attention in the last decade. This paper is devoted to exploring plane-symmetric solutions in the context of metric f(R) gravity. We extend the work on static plane-symmetric vacuum solutions in f(R) gravity already available in the literature [1, 2]. The modified field equations are solved using the assumptions of both constant and nonconstant scalar curvature. Some well-known solutions are recovered with power-law and logarithmic forms of f(R) models.     

Dark Energy Models in <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">R</Emphasis>, <Emphasis Type="Italic">T</Emphasis>) Theory with Variable Deceleration Parameter

In this communication we have investigated Bianchi type-II dark energy (DE) cosmological models with and without presence of magnetic field in modified f(R, T) gravity theory as proposed by Harko et al. (Phys. Rev. D, 84, 024020, 2011). The exact solution of the field equations is obtained by setting the deceleration parameter q as a time function along with suitable assumption the scale factor \(a(t)= [sinh(\alpha t)]^{\frac {1}{n}}\), α and n are positive constant. We have obtained a class of accelerating and decelerating DE cosmological models for different values of n and α. The present study believes that the mysterious dark energy is the main responsible force for accelerating expansion of the universe. For our constructed models the DE candidates cosmological constant (Λ) and the EoS parameter (ω) both are found to be time varying quantities. The cosmological constant Λ is very large at early time and approaches to a small positive value at late time whereas the EoS parameters is found small negative at present time. Physical and kinematical properties of the models are discussed with the help of pictorial representations of the parameters. We have observed that our constructed models are compatible with recent cosmological observations.     

Black-hole solutions in <Emphasis Type="Italic">F</Emphasis>(<Emphasis Type="Italic">R</Emphasis>) gravity with conformal anomaly

In this paper, we consider F(R)=R+f(R) theory instead of Einstein gravity with conformal anomaly and look for its analytical solutions. Depending on the free parameters, one may obtain both uncharged and charged solutions for some classes of F(R) models. Calculation of Kretschmann scalar shows that there is a singularity located at r=0. The geometry of uncharged (charged) solution corresponds to the Schwarzschild (Reissner–Nordström) singularity. Further, we discuss the viability of our models in detail. We show that these models can be stable, depending on their parameters and in different epochs of the universe.     

The <Emphasis Type="Italic">q</Emphasis>-boson-fermion realizations of the quantum superalgebra <Emphasis Type="Italic">U</Emphasis><Subscript><Emphasis Type="Italic">q</Emphasis></Subscript>(<Emphasis Type="Italic">osp</Emphasis>(1/2))

We show that our construction of realizations for algebras and quantum algebras can be generalized to quantum superalgebras too. We studyan example of quantum superalgebra U _q (osp(1/2)) and give the boson-fermion realization with respect to one pair of q-boson operators and one pair of fermions.     

Graviton and scalar propagations on AdS<Subscript>4</Subscript> space in <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">R</Emphasis>) gravities

We investigate propagations of graviton and additional scalar on four-dimensional anti-de Sitter (AdS₄) space using f(R) gravity models with external sources. It is shown that there is the van Dam–Veltman–Zakharov (vDVZ) discontinuity in f(R) gravity models because f(R) gravity implies GR with additional scalar. This clearly indicates a difference between general relativity and f(R) gravity.     

<Emphasis Type="Italic">O</Emphasis>(1) eV sterile neutrino in <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">R</Emphasis>) gravity

We refer [1] to the role of an additional O(1) eV sterile neutrino in modified gravity models. We find parameter constraints in particular f(R) gravity model using following up-to-dated cosmological data: measurements of the cosmic microwave background (CMB) anisotropy, the CMB lensing potential, the baryon acoustic oscillations (BAO), the cluster mass function and the Hubble constant. It was obtained for the sterile neutrino mass 0.47 eV < m _ν,sterile < 1 eV (2σ) assuming that the sterile neutrinos are thermalized and the active neutrinos are massless, not significantly larger than in the standard cosmology model within the same data set: 0.45 eV < m _ν,sterile < 0.92 eV (2σ). But, if the mass of sterile neutrino is fixed and equals ≈ 1.5 eV according to various anomalies in neutrino oscillation experiments, f(R) gravity is much more consistent with observation data than the CDM model.     

Efficient Nonlocal <Emphasis Type="Italic">M</Emphasis>-Control and <Emphasis Type="Italic">N</Emphasis>-Target Controlled Unitary Gate Using Non-symmetric GHZ States

Efficient local implementation of a nonlocal M-control and N-target controlled unitary gate is considered. We first show that with the assistance of two non-symmetric qubit⁽¹⁾-qutrit^(N) Greenberger-Horne-Zeilinger (GHZ) states, a nonlocal 2-control and N-target controlled unitary gate can be constructed from 2 local two-qubit CNOT gates, 2N local two-qutrit conditional SWAP gates, N local qutrit-qubit controlled unitary gates, and 2N single-qutrit gates. At each target node, the two third levels of the two GHZ target qutrits are used to expose one and only one initial computational state to the local qutrit-qubit controlled unitary gate, instead of being used to hide certain states from the conditional dynamics. This scheme can be generalized straightforwardly to implement a higher-order nonlocal M-control and N-target controlled unitary gate by using M non-symmetric qubit⁽¹⁾-qutrit^(N) GHZ states as quantum channels. Neither the number of the additional levels of each GHZ target particle nor that of single-qutrit gates needs to increase with M. For certain realistic physical systems, the total gate time may be reduced compared with that required in previous schemes.