Existence of periodic solutions for the Lotka-Volterra type systems

In this paper we prove the existence of non-stationary periodic solutions of delay Lotka-Volterra equations. In the proofs we use the degree for $S^1$-equivariant maps

Electromagnetic Spectrum from QGP Fluid

We calculate thermal photon and electron pair distribution from hot QCD matter produced in high energy heavy-ion collisions, based on a hydrodynamical model which is so tuned as to reproduce the recent experimental data at CERN SPS, and compare these electromagnetic spectra with experimental data given by CERN WA80 and CERES. We investigate mainly the effects of the off-shell properties of the source particles on the electromagnetic spectra.Comment: 5 pages, latex, 4 Postscript figures. A talk given at the International School on the Physics of Quark Gluon Plasma, June 3-6, 1997, Hiroshima, Japan. To be appeared in Prog. Theor. Phys. Supplemen

On the scalar graviton in n-DBI gravity

n-DBI gravity is a gravitational theory which yields near de Sitter inflation spontaneously at the cost of breaking Lorentz invariance by a preferred choice of foliation. We show that this breakdown endows n-DBI gravity with one extra physical gravitational degree of freedom: a scalar graviton. Its existence is established by Dirac's theory of constrained systems. Firstly, studying scalar perturbations around Minkowski space-time, we show that there exists one scalar degree of freedom and identify it in terms of the metric perturbations. Then, a general analysis is made in the canonical formalism, using ADM variables. It is useful to introduce an auxiliary scalar field, which allows recasting n-DBI gravity in an Einstein-Hilbert form but in a Jordan frame. Identifying the constraints and their classes we confirm the existence of an extra degree of freedom in the full theory, besides the two usual tensorial modes of the graviton. We then argue that, unlike the case of (the original proposal for) Horava-Lifschitz gravity, there is no evidence that the extra degree of freedom originates pathologies, such as vanishing lapse, instabilities and strong self-coupling at low energy scales.Comment: 30 pages, 1 figur

Observational Constraints on Phantom Crossing DGP Gravity

We study the observational constraints on the Phantom Crossing DGP model. We demonstrate that the crossing of the phantom divide does not occur within the framework of the original Dvali-Gabadadze-Porrati (DGP) model or the DGP model developed by Dvali and Turner. By extending their model in the framework of an extra dimension scenario, we study a model that realizes crossing of the phantom divide. We investigate the cosmological constraints obtained from the recent observational data of Type Ia Supernovae, Cosmic Microwave Background anisotropies, and Baryon Acoustic Oscillations. The best fit values of the parameters with 1$\sigma$ (68%) errors for the Phantom Crossing DGP model are $\Omega_{m,0}=0.27^{+0.02}_{-0.02}$, $\beta=0.54^{+0.24}_{-0.30}$. We find that the Phantom Crossing DGP model is more compatible with the observations than the original DGP model or the DGP model developed by Dvali and Turner. Our model can realize late-time acceleration of the universe, similar to that of $\Lambda$CDM model, without dark energy due to the effect of DGP gravity. In our model, crossing of the phantom divide occurs at a redshift of $z \sim 0.2$.Comment: 17 pages, 9 figures, 1 table, Accepted for publication in International Journal of Modern Physics