Supernova constraints on higher-dimensional cosmology with a phantom field

We use observational data on the magnitude-redshift relation for Type Ia supernovae together with constraints on the ages of the oldest stars to rule out a higher-dimensional extension of General Relativity with a negative kinetic-energy scalar field. This theory is of considerable physical interest because it produces accelerated expansion at both early and late times with a single new field, as in quintessential inflation scenarios. It is also of mathematical interest because it is characterized by an analytic expression for the macroscopic scale factor $a(t)$. We show that cosmological solutions of this theory can be usefully parametrized by a single quantity, the lookback time $\tau_{\text{tr}}$ corresponding to the transition from deceleration to acceleration. Supernovae data from the recently released Supernova Cosmology Project Union 2.1 compilation single out a narrow range of values for $\tau_{\text{tr}}$. In the context of the theory, however, these same values of $\tau_{\text{tr}}$ imply that the universe is much older than the oldest observed stars.Comment: 10 pages, 5 figure

Asymptotically Static Universe

We consider a cosmology in which the final stage of the Universe is neither accelerating nor decelerating, but approaches an asymptotic state where the scale factor becomes a constant value. In order to achieve this, we first bring in a scale factor with the desired property and then determine the details of the energy contents as a result of the cosmological evolution equations. We show that such a scenario can be realized if we introduce a generalized quintom model which consists of a scalar field and a phantom with a {\it negative} cosmological constant term. The standard cold dark matter with $w_m=0$ is also introduced. This is possible basically due to the balance between the matter and the {\it negative} cosmological constant which tend to attract and scalar field and phantom which repel in the asymptotic region. The stability analysis shows that this asymptotic solution is classically stable.Comment: Final version published in PR

Conformally-coupled dark spinor and FRW universe

We study conformal coupling of dark spinor fields to gravity and calculate the energy density and the pressure of the spinor in FRW spacetime. We consider the renormalizable potential of the spinor field. In the cases where the field is proportional to some power of the cosmic scale factor $a(t)$, we determine the Hubble parameter as a function of the scale factor and find analytic solutions for $a(t)$ when the spinor field matter dilutes as the universe expands. We discuss the possibility that both matter- and dark energy-dominated eras of our universe can be described by the dark spinor.Comment: 4 pages, Revised argument in section III, results unchanged. To be published in PR

Isospin particle on S2S^{2} with arbitrary number of supersymmetries

We study the supersymmetric quantum mechanics of an isospin particle in the background of spherically symmetric Yang-Mills gauge field. We show that on $S^{2}$ the number of supersymmetries can be made arbitrarily large for a specific choice of the spherically symmetric SU(2) gauge field. However, the symmetry algebra containing the supercharges becomes nonlinear if the number of fermions is greater than two. We present the exact energy spectra and eigenfunctions, which can be written as the product of monopole harmonics and a certain isospin state. We also find that the supersymmetry is spontaneously broken if the number of supersymmetries is even.Comment: 6 page

Alterations in Striatal Circuits Underlying Addiction-Like Behaviors

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N=4 Supersymmetric Quantum Mechanics with Magnetic Monopole

We propose an N=4 supersymmetric quantum mechanics of a charged particle on a sphere in the background of Dirac magnetic monopole and study the system using the CP(1) model approach. We explicitly calculate the symmetry algebra taking the operator ordering ambiguity into consideration. We find that it is given by the superalgebra SU(1|2)x SU(2). We show that the Hamiltonian can be written in terms of the Casimir invariant of SU(2). Using this relation and the lower bound for angular momentm we obtain the energy spectrum. We then examine the ground energy sector to find that the N=4 supersymmetry is spontaneously broken to N=2 for certain values of the monopole charge.Comment: 7 page

Gauge symmetry enhancement in Hamiltonian formalism

We study the Hamiltonian structure of the gauge symmetry enhancement in the enlarged CP(N) model coupled with U(2) Chern-Simons term, which contains a free parameter governing explicit symmetry breaking and symmetry enhancement. After giving a general discussion of the geometry of constrained phase space suitable for the symmetry enhancement, we explicitly perform the Dirac analysis of our model and compute the Dirac brackets for the symmetry enhanced and broken cases. We also discuss some related issues.Comment: 8 pages, typos correcte