Constraining cosmological parameters with observational data including weak lensing effects

In this Letter, we study the cosmological implications of the 100 square degree Weak Lensing survey (the CFHTLS-Wide, RCS, VIRMOS-DESCART and GaBoDS surveys). We combine these weak lensing data with the cosmic microwave background (CMB) measurements from the WMAP5, BOOMERanG, CBI, VSA, ACBAR, the SDSS LRG matter power spectrum and the Type Ia Supernoave (SNIa) data with the “Union” compilation (307 sample), using the Markov Chain Monte Carlo method to determine the cosmological parameters, such as the equation-of-state (EoS) of dark energy w  , the density fluctuation amplitude σ₈${\sigma }_8$, the total neutrino mass ∑mν$\sum m_{\nu }$ and the parameters associated with the power spectrum of the primordial fluctuations. Our results show that the ΛCDM model remains a good fit to all of these data. In a flat universe, we obtain a tight limit on the constant EoS of dark energy, w=−0.97±0.041$w=-0.97\pm 0.041$ (1σ  ). For the dynamical dark energy model with time evolving EoS parameterized as wde(a)=w₀+wa(1−a)$w_{\mathrm{de}}(a)=w_0+w_a(1-a)$, we find that the best-fit values are w₀=−1.064$w_0=-1.064$ and wa=0.375$w_a=0.375$, implying the mildly preference of Quintom model whose EoS gets across the cosmological constant boundary during evolution. Regarding the total neutrino mass limit, we obtain the upper limit, ∑mν<0.471 eV$\sum m_{\nu }<0.471\text{eV}$ (95% C.L.) within the framework of the flat ΛCDM model. Due to the obvious degeneracies between the neutrino mass and the EoS of dark energy model, this upper limit will be relaxed by a factor of 2 in the framework of dynamical dark energy models. Assuming that the primordial fluctuations are adiabatic with a power law spectrum, within the ΛCDM model, we find that the upper limit on the ratio of the tensor to scalar is r<0.35$r<0.35$ (95% C.L.) and the inflationary models with the slope ns?1$n_s?1$ are excluded at more than 2σ   confidence level. In this Letter we pay particular attention to the contribution from the weak lensing data and find that the current weak lensing data do improve the constraints on matter density Ωm${\Omega }_m$, σ₈${\sigma }_8$, ∑mν$\sum m_{\nu }$, and the EoS of dark energy.     

Hadro-charmonium

We argue that relatively compact charmonium states, J/ψ$J/\psi$, ψ(2S)$\psi (2S)$, χc${\chi }_c$, can very likely be bound inside light hadronic matter, in particular inside higher resonances made from light quarks and/or gluons. The charmonium state in such binding essentially retains its properties, so that the bound system decays into light mesons and the particular charmonium resonance. Thus such bound states of a new type, which we call hadro-charmonium, may explain the properties of some of the recently observed resonant peaks, in particular of Y(4.26)$Y(4.26)$, Y(4.32–4.36)$Y(4.32\text{–}4.36)$, Y(4.66)$Y(4.66)$, and Z(4.43)$Z(4.43)$. We discuss further possible implications of the suggested picture for the observed states and existence of other states of hadro-charmonium and hadro-bottomonium.     

Vacuum phase transition at nonzero baryon density

It is argued that the dominant contribution to the interaction of quark–gluon plasma at moderate T?Tc$T?T_c$ is given by the nonperturbative vacuum field correlators. Basing on that nonperturbative equation of state of quark–gluon plasma is computed and in the lowest approximation expressed in terms of absolute values of Polyakov lines for quarks and gluons Lfund(T),Ladj(T)=(Lfund)^9/4$L_{\mathrm{fund}}(T),L_{\mathrm{adj}}(T)={(L_{\mathrm{fund}})}^{9/4}$ known from lattice and analytic calculations. Phase transition at any μ   is described as a transition due to vanishing of one of correlators, DE(x)$D^E(x)$, which implies the change of gluonic condensate ΔG₂$\mathrm{\Delta }{G}_2$. Resulting transition temperature Tc(μ)$T_c(\mu )$ is calculated in terms of ΔG₂$\mathrm{\Delta }{G}_2$ and Lfund(Tc)$L_{\mathrm{fund}}(T_c)$. The phase curve Tc(μ)$T_c(\mu )$ is in a good agreement with lattice data. In particular Tc(0)=0.27$T_c(0)=0.27$; 0.19; 0.17 GeV$0.17\text{ GeV}$ for nf=0,2,3$n_f=0,2,3$ and fixed ΔG₂=0.0035 GeV⁴$\mathrm{\Delta }{G}_2=0.0035{\text{ GeV}}^4$.     

Dynamical SUSY breaking in heterotic M-theory

It is shown that four-dimensional N=1$N=1$ supersymmetric QCD with massive flavors in the fundamental representation of the gauge group can be realized in the hidden sector of E₈×E₈$E_8\times E_8$ heterotic string vacua. The number of flavors can be chosen to lie in the range of validity of the free-magnetic dual, using which one can demonstrate the existence of long-lived meta-stable non-supersymmetric vacua. This is shown explicitly for the gauge group Spin(10)$\mathit{Spin}(10)$, but the methods are applicable to Spin(Nc)$\mathit{Spin}(N_c)$, SU(Nc)$\mathit{SU}(N_c)$ and Sp(Nc)$\mathit{Sp}(N_c)$ for a wide range of color index Nc$N_c$. Hidden sectors of this type can potentially be used as a mechanism to break supersymmetry within the context of heterotic M-theory.     

Probing dark energy using its density instead of its equation of state

The variation of dark energy density with redshift, ρX(z)${\rho }_X(z)$, provides a critical clue to the nature of dark energy. Since ρX(z)${\rho }_X(z)$ depends on the dark energy equation of state wX(z)$w_X(z)$ through an integral, ρX(z)${\rho }_X(z)$ can be constrained more tightly than wX(z)$w_X(z)$ given the same observational data. We demonstrate this explicitly using current type Ia supernova (SN Ia) data [the Tonry/Barris sample], together with the Cosmic Microwave Background (CMB) shift parameter from CMB data (WMAP, CBI, and ACBAR), and the large scale structure (LSS) growth factor from 2dF galaxy survey data. We assume a flat universe, and use Markov Chain Monte Carlo (MCMC) technique in our analysis. We find that, while wX(z)$w_X(z)$ extracted from current data is consistent with a cosmological constant at 68% C.L., ρX(z)${\rho }_X(z)$ (which has far smaller uncertainties) is not. Our results clearly show the advantage of using ρX(z)${\rho }_X(z)$, instead of wX(z)$w_X(z)$, to probe the variation of dark energy.     

Quantum Regge Calculus of Einstein–Cartan theory

We study the Quantum Regge Calculus of Einstein–Cartan theory to describe quantum dynamics of Euclidean space–time discretized as a 4-simplices complex. Tetrad field eμ(x)$e_{\mu }(x)$ and spin-connection field ωμ(x)${\omega }_{\mu }(x)$ are assigned to each 1-simplex. Applying the torsion-free Cartan structure equation to each 2-simplex, we discuss parallel transports and construct a diffeomorphism and local   gauge-invariant Einstein–Cartan action. Invariant holonomies of tetrad and spin-connection fields along large loops are also given. Quantization is defined by a bounded partition function with the measure of SO(4)$\mathit{SO}(4)$-group valued ωμ(x)${\omega }_{\mu }(x)$ fields and Dirac-matrix valued eμ(x)$e_{\mu }(x)$ fields over 4-simplices complex.     

Partition function zeros of the antiferromagnetic Ising model on triangular lattice in the complex temperature plane for nonzero magnetic field

The grand partition functions Z(T,B)$Z(T,B)$ of the Ising model on L×L$L\times L$ triangular lattices with fully periodic boundary conditions, as a function of temperature T and magnetic field B  , are evaluated exactly for L<12$L<12$ (using microcanonical transfer matrix) and approximately for L?12$L?12$ (using Wang–Landau Monte Carlo algorithm). From Z(T,B)$Z(T,B)$, the distributions of the partition function zeros of the triangular-lattice Ising model in the complex temperature plane for real B≠0$B\ne 0$ are obtained and discussed for the first time. The critical points aN(x)$a_N(x)$ and the thermal scaling exponents yt(x)$y_t(x)$ of the triangular-lattice Ising antiferromagnet, for various values of x=e−2βB$x=e^{-2\beta B}$, are estimated using the partition function zeros.     

First-order density matrices in one dimension for independent fermions and impenetrable bosons in harmonic traps

To complement existing knowledge of the density matrix γF(x,y)${\gamma }_{\mathrm{F}}(x,y)$ of independent fermions for N   particles in one dimension under harmonic confinement, the corresponding matrix γIB(x,y)${\gamma }_{\mathrm{IB}}(x,y)$ for impenetrable bosons is given for N=2$N=2$ and 3 (with the N=4$N=4$ form available also). For fermions the momentum density is then obtained and illustrated numerically for N=10$N=10$. The boson momentum density is studied analytically at high momentum p  , the coefficients of the p⁻⁴$p^{\mathrm{-4}}$ and p⁻⁶$p^{\mathrm{-6}}$ terms being tabulated for N=2–5$N=2\text{–}5$ inclusive. Their dependence on powers of N   is exhibited numerically. Finally, the functional relationship between γIB(x,y)${\gamma }_{\mathrm{IB}}(x,y)$ and γF(x,y)${\gamma }_{\mathrm{F}}(x,y)$ is formally set out and illustrated.     

If Gauss–Bonnet interaction plays the role of dark energy

A cosmological model has been constructed with Gauss–Bonnet-scalar interaction, where the Universe starts with exponential expansion but encounters infinite deceleration, q→∞$q\to \infty$ and infinite equation of state parameter, w→∞$w\to \infty$. During evolution it subsequently passes through the stiff fluid era, q=2$q=2$, w=1$w=1$, the radiation dominated era, q=1$q=1$, w=1/3$w=1/3$ and the matter dominated era, q=1/2$q=1/2$, w=0$w=0$. Finally, deceleration halts, q=0$q=0$, w=−1/3$w=-1/3$, and it then encounters a transition to the accelerating phase. Asymptotically the Universe reaches yet another inflationary phase q→−1$q\to -1$, w→−1$w\to -1$. Such evolution is independent of the form of the potential and the sign of the kinetic energy term, i.e., even a non-canonical kinetic energy is unable to phantomize (w<−1)$(w<-1)$ the model.     

Can density functional theory make use of experimentally determined ground-state electron densities via the Dirac density matrix for molecules of biological interest?

More than four decades ago, March and Murray gave a perturbation theory of the single-particle(s) Dirac density matrix γs(r,r^′)${\gamma }_s(r,r^{\prime })$ to all orders in a given one-body potential energy V(r)$V(r)$. However, for density functional theory in orbital-free form, one requires the functional γs[ρ]${\gamma }_s[\rho ]$ where ρ(r)$\rho (r)$ is the ground-state electron density. Therefore, in the present study, a first-order non-linear differential equation is proposed for γs${\gamma }_s$ in terms of ρ(r)$\rho (r)$ and ∇ρ(r)$\mathrm{\nabla }\rho (r)$, plus the single-particle kinetic energy. Since this latter quantity is itself known to be a functional of ρ  , the existence of such an equation for γs${\gamma }_s$ would be a significant step along the road to determining the desired functional γs[ρ]${\gamma }_s[\rho ]$. As yet, we have succeeded in giving a rigorous proof of the proposed differential equation for γs(r,r^′)${\gamma }_s(r,r^{\prime })$ only for one- and two-level molecules. If it is subsequently proved for an arbitrary number of levels, which we believe should be possible, it would then allow γs${\gamma }_s$ to be calculated for molecules of biological interest, from experimentally measured ground-state densities ρ(r)$\rho (r)$, as the approach is entirely orbital-free.     

Single eta production in heavy quarkonia: Breakdown of multipole expansion

The η   production in the (n,n^′)$(n,n^{\prime })$ bottomonium transitions ?(n)→?(n^′)η$?(n)\to ?(n^{\prime })\eta$, is studied in the method used before for dipion heavy quarkonia transitions. The widths Γη(n,n^′)${\Gamma }_{\eta }(n,n^{\prime })$ are calculated without fitting parameters for n=2,3,4,5$n=2,3,4,5$, n^′=1$n^{\prime }=1$. Resulting Γη(4,1)${\Gamma }_{\eta }(4,1)$ is found to be large in agreement with recent data. Multipole expansion method is shown to be inadequate for large size systems considered.     

Discrete gauge symmetries in discrete MSSM-like orientifolds

Motivated by the necessity of discrete _ZN${\mathbb{Z}}_N$ symmetries in the MSSM to insure baryon stability, we study the origin of discrete gauge symmetries from open string sector U(1)$U(1)$?s in orientifolds based on rational conformal field theory. By means of an explicit construction, we find an integral basis for the couplings of axions and U(1)$U(1)$ factors for all simple current MIPFs and orientifolds of all 168 Gepner models, a total of 32 990 distinct cases. We discuss how the presence of discrete symmetries surviving as a subgroup of broken U(1)$U(1)$?s can be derived using this basis. We apply this procedure to models with MSSM chiral spectrum, concretely to all known U(3)×U(2)×U(1)×U(1)$U(3)\times U(2)\times U(1)\times U(1)$ and U(3)×Sp(2)×U(1)×U(1)$U(3)\times \mathit{Sp}(2)\times U(1)\times U(1)$ configurations with chiral bi-fundamentals, but no chiral tensors, as well as some SU(5)$\mathit{SU}(5)$ GUT models. We find examples of models with _Z2${\mathbb{Z}}_2$ (R-parity) and _Z3${\mathbb{Z}}_3$ symmetries that forbid certain B and/or L violating MSSM couplings. Their presence is however relatively rare, at the level of a few percent of all cases.     

Constraints on kinematic models from the latest observational data

Kinematical models are constrained by the latest observational data from geometry-distance measurements, which include 557 type Ia supernovae (SNIa) Union2 data and 15 observational Hubble data. Considering two parameterized deceleration parameter, the values of current deceleration parameter q₀$q_0$, jerk parameter j₀$j_0$ and transition redshift zT$z_T$, are obtained. Furthermore, we show the departures for two parameterized kinematical models from ΛCDM model according to the evolutions of jerk parameter j(z)$j(z)$. Also, it is shown that the constraint on jerk parameter j(z)$j(z)$ is weak by the current geometrical observed data.     

Transition between SU(4) and SU(2) Kondo effect

Motivated by experiments in nanoscopic systems, we study a generalized Anderson, which consist of two spin degenerate doublets hybridized to a singlet by the promotion of an electron to two conduction bands, as a function of the energy separation δ$\delta$ between both doublets. For δ=0$\delta =0$ or very large, the model is equivalent to a one-level SU(N$N$) Anderson model, with N=4$N=4$ and 2 respectively. We study the evolution of the spectral density for both doublets (ρ_1σ(ω)${\rho }_{1\sigma }(\omega )$ and ρ_2σ(ω)${\rho }_{2\sigma }(\omega )$) and their width in the Kondo limit as δ$\delta$ is varied, using the non-crossing approximation (NCA). As δ$\delta$ increases, the peak at the Fermi energy in the spectral density (Kondo peak) splits and the density of the doublet of higher energy ρ_2σ(ω)${\rho }_{2\sigma }(\omega )$ shifts above the Ferrmi energy. The Kondo temperature T_K (determined by the half-width at half maximum of the Kondo peak in density of the doublet of lower energy ρ_1σ(ω)${\rho }_{1\sigma }(\omega )$) decreases dramatically. The variation of T_K with δ$\delta$ is reproduced by a simple variational calculation.