Modeling Galactic Halos with Predominantly Quintessential Matter

This paper discusses a new model for galactic dark matter by combining an anisotropic pressure field corresponding to normal matter and a quintessence dark energy field having a characteristic parameter ω _q such that -1 < w_q < -\frac13-1<\omega_{q}< -\frac{1}{3}. Stable stellar orbits together with an attractive gravity exist only if ω _q is extremely close to -\frac13-\frac{1}{3}, a result consistent with the special case studied by Guzman et al. (Rev. Mex. Fis. 49:303, 2003). Less exceptional forms of quintessence dark energy do not yield the desired stable orbits and are therefore unsuitable for modeling dark matter.     

Genesis of Dark Energy: Dark Energy as Consequence of Release and Two-Stage Tracking of Cosmological Nuclear Energy

Recent observations on Type-Ia supernovae and low density (Ω _m =0.3) measurement of matter including dark matter suggest that the present-day universe consists mainly of repulsive-gravity type ‘exotic matter’ with negative-pressure often said ‘dark energy’ (Ω _x =0.7). But the nature of dark energy is mysterious and its puzzling questions, such as why, how, where and when about the dark energy, are intriguing. In the present paper the authors attempt to answer these questions while making an effort to reveal the genesis of dark energy and suggest that ‘the cosmological nuclear binding energy liberated during primordial nucleo-synthesis remains trapped for a long time and then is released free which manifests itself as dark energy in the universe’. It is also explained why for dark energy the parameter w=-\frac23w=-\frac{2}{3} . Noting that w=1 for stiff matter and w=\frac13w=\frac{1}{3} for radiation; w=-\frac23w=-\frac{2}{3} is for dark energy because “−1” is due to ‘deficiency of stiff-nuclear-matter’ and that this binding energy is ultimately released as ‘radiation’ contributing “ +\frac13+\frac{1}{3} ”, making w=-1+\frac13=-\frac23w=-1+\frac{1}{3}=-\frac{2}{3} . When dark energy is released free at Z=80, w=-\frac23w=-\frac{2}{3} . But as on present day at Z=0 when the radiation-strength-fraction (δ), has diminished to δ→0, the w=-1+d\frac13=-1w=-1+\delta\frac{1}{3}=-1 . This, almost solves the dark-energy mystery of negative pressure and repulsive-gravity. The proposed theory makes several estimates/predictions which agree reasonably well with the astrophysical constraints and observations. Though there are many candidate-theories, the proposed model of this paper presents an entirely new approach (cosmological nuclear energy) as a possible candidate for dark energy.     

Interacting polytropic gas model of phantom dark energy in?non-flat universe

By introducing the polytropic gas model of interacting dark energy, we obtain the equation of state for the polytropic gas energy density in a non-flat universe. We show that for an even polytropic index by choosing $K>Ba^{\frac{3}{n}}$K>Ba^{\frac{3}{n}} , one can obtain ω _Λ ^eff<−1, which corresponds to a universe dominated by phantom dark energy.     

Unifying dark energy and dark matter with the modified Ricci model

In this paper, two modified Ricci models are considered as the candidates of unified dark matter–dark energy. In model one, the energy density is given by r_MR=3M_pl(aH²+b[(H)\dot])\rho_{\mathrm{MR}}=3M_{\mathrm{pl}}(\alpha H^{2}+\beta\dot{H}), whereas, in model two, by r_MR=3M_pl(\fraca6 R+g[(H)\ddot]H^-1)\rho_{\mathrm{MR}}=3M_{\mathrm{pl}}(\frac{\alpha}{6} R+\gamma\ddot{H}H^{-1}). We find that they can explain both dark matter and dark energy successfully. A constant equation of state of dark energy is obtained in model one, which means that it gives the same background evolution as the wCDM model, while model two can give an evolutionary equation of state of dark energy with the phantom divide line crossing in the near past.     

Five Dimensional Cosmological Models in General Relativity

A five dimensional Kaluza-Klein space-time is considered in the presence of a perfect fluid source with variable G and Λ. An expanding universe is found by using a relation between the metric potential and an equation of state. The gravitational constant is found to decrease with time as G∼t ^−(1−ω) whereas the variation for the cosmological constant follows as Λ∼t ⁻², L ~ ([(R)\dot]/R)²\Lambda \sim (\dot{R}/R)^{2} and L ~ [(R)\ddot]/R\Lambda \sim \ddot{R}/R where ω is the equation of state parameter and R is the scale factor.     

Revisiting generalized Chaplygin gas as a unified dark matter and dark energy model

In this paper, we revisit the generalized Chaplygin gas (GCG) model as a unified dark matter and dark energy model. The energy density of GCG model is given as ρ _GCG/ρ _GCG0=[B _s +(1−B _s )a ^−3(1+α)]^1/(1+α), where α and B _s are two model parameters which will be constrained by type Ia supernova as standard candles, baryon acoustic oscillation as standard rulers and the seventh year full WMAP data points. In this paper, we will not separate GCG into dark matter and dark energy parts any more as adopted in the literature. By using the Markov Chain Monte Carlo method, we find the results a = 0.00126_{-0.00126- 0.00126}^{+ 0.000970+ 0.00268}\alpha=0.00126_{-0.00126- 0.00126}^{+ 0.000970+ 0.00268} and B_s = 0.775_{-0.0161- 0.0338}^{+ 0.0161+ 0.0307}B_{s}= 0.775_{-0.0161- 0.0338}^{+ 0.0161+ 0.0307}.     

Stability of One-Electron Molecules in the Brown–Ravenhall Model

In appropriate units, the Brown-Ravenhall Hamiltonian for a system of 1 electron relativistic molecules with K fixed nuclei having charge and position Zk, R_k, k=1,2, ?,Kk=1,2, \ldots,K, is of the form \bB_1,K = L₊ ( D₀ + aV_c) L₊ \bB_{1,K}= \Lambda_+ \bigl( D_0 + \alpha V_c\bigr) \Lambda_+ , where v₊ is the projection onto the positive spectral subspace of the free Dirac operator D₀ and V_c = - ?_k=1^K \fracaZ_k\lmod \bx-R_k \rmod + ?_{k < l,  k,l=1}^K \fracaZ_k Z_l\lmod R_k-R_l \rmod V_c= - \sum_{k=1}^K \frac{\alpha Z_k}{\lmod \bx-R_k \rmod} + \sum_{kZ_k ￡ aZ_c = \frac2p/2 + 2/ p\alpha Z_k \leq \alpha Z_c = \frac{2}{\pi /2 + 2/ \pi}, k=1,2, ?,Kk=1,2, \ldots,K, and a ￡ \frac2 p(p²+4)(2+?{1+ p/2})\alpha \leq \frac{2 \pi}{(\pi^2+4)(2+\sqrt{1+ \pi /2})}, \ \bB_1,K 3 \operatornameconst \cdotp K\bB_{1,K} \geq \operatorname{const} \cdotp K.     

Critical Hardy–Lieb–Thirring Inequalities for Fourth-Order Operators in Low Dimensions

This paper considers Hardy–Lieb–Thirring inequalities for higher order differential operators. A result for general fourth-order operators on the half-line is developed, and the trace inequality

Phenomenology of Λ-CDM Model: A?Possibility of?Accelerating Universe with Positive Pressure

Among various phenomenological Λ models, a time-dependent model [(L)\dot] ~ H³\dot{\Lambda}\sim H^{3} is selected here to investigate the Λ-CDM cosmology. The model can follow from dynamics, underlying the origin of Λ. Using this model the expressions for the time-dependent equation of state parameter ω and other physical parameters are derived. It is shown that in H ³ model accelerated expansion of the Universe takes place at negative energy density, but with a positive pressure. It has also been possible to obtain the change of sign of the deceleration parameter q during cosmic evolution.     

Global Solutions to the 3-D Incompressible Anisotropic Navier-Stokes System in the Critical Spaces

In this paper, we consider the global wellposedness of the 3-D incompressible anisotropic Navier-Stokes equations with initial data in the critical Besov-Sobolev type spaces B{\mathcal{B}} and B^{-\frac12,\frac12}₄{\mathcal{B}^{-\frac12,\frac12}_4} (see Definitions 1.1 and 1.2 below). In particular, we proved that there exists a positive constant C such that (ANS _ν ) has a unique global solution with initial data u₀ = (u₀^h, u₀³){u_0 = (u_0^h, u_0^3)} which satisfies ||u₀^h||_B exp(\fracCn⁴ ||u₀³||_B⁴) ￡ c₀n{\|u_0^h\|_{\mathcal{B}} \exp\bigl(\frac{C}{\nu^4} \|u_0^3\|_{\mathcal{B}}^4\bigr) \leq c_0\nu} or ||u₀^h||_{B^{-\frac12,\frac12}4} exp(\fracCn⁴ ||u₀³||_{B^{-\frac12,\frac12}4}⁴) ￡ c₀n{\|u_0^h\|_{\mathcal{B}^{-\frac12,\frac12}_{4}} \exp \bigl(\frac{C}{\nu^4} \|u_0^3\|_{\mathcal{B}^{-\frac12,\frac12}_{4}}^4\bigr)\leq c_0\nu} for some c ₀ sufficiently small. To overcome the difficulty that Gronwall’s inequality can not be applied in the framework of Chemin-Lerner type spaces, [(L^p_t)\tilde](B){\widetilde{L^p_t}(\mathcal{B})}, we introduced here sort of weighted Chemin-Lerner type spaces, [(L²_{t, f})\tilde](B){\widetilde{L^2_{t, f}}(\mathcal{B})} for some apropriate L ¹ function f(t).     

Anisotropic Universe Models with Perfect Fluid and Dark Energy with Time Varying G and Λ

We have investigated general Bianchi type I cosmological models which containing a perfect fluid and dark energy with time varying G and Λ that have been presented. The perfect fluid is taken to be one obeying the equation of state parameter, i.e., p=ωρ; whereas the dark energy density is considered to be either modified polytropic or the Chaplygin gas. Cosmological models admitting both power-law which is explored in the presence of perfect fluid and dark energy too. We reconstruct gravitational parameter G, cosmological term Λ, critical density ρ _c , density parameter Ω, cosmological constant density parameter Ω _Λ and deceleration parameter q for different equation of state. The present study will examine non-linear EOS with a general nonlinear term in the energy density.     

Time-resolved photoelectron spectroscopy on small tungsten cluster anions

We have studied the dynamics of photoexcited tungsten cluster anions W_n^-\mathrm{W}_{n}^{-} (n=3,4,…,14) by means of time-resolved two-photon photodetachment spectroscopy. At an excitation energy of h ν _pump=1.56 eV the photoinduced dynamics is mainly dominated by fast electronic relaxation processes. For the smallest clusters, i.e., W₃^-\mathrm{W}_{3}^{-}, W₄^-\mathrm{W}_{4}^{-}, and W₅^-\mathrm{W}_{5}^{-}, individual relaxation channels have been identified and resolved on a timescale well below 100 fs. The time constants for the decay of nascent and secondary electrons have been deduced from a Bloch model. Complete thermalization takes place for all clusters on a timescale of ∼1 ps.     

Critical Rotational Speeds in the Gross-Pitaevskii Theory on a Disc with Dirichlet Boundary Conditions

We study the two-dimensional Gross-Pitaevskii theory of a rotating Bose gas in a disc-shaped trap with Dirichlet boundary conditions, generalizing and extending previous results that were obtained under Neumann boundary conditions. The focus is on the energy asymptotics, vorticity and qualitative properties of the minimizers in the parameter range |log ε|≪Ω≲ε ⁻²|log ε|⁻¹ where Ω is the rotational velocity and the coupling parameter is written as ε ⁻² with ε≪1. Three critical speeds can be identified. At \varOmega = \varOmega_c1 ~ |loge|\varOmega=\varOmega_{\mathrm{c_{1}}}\sim |\log\varepsilon| vortices start to appear and for |loge| << \varOmega < \varOmega_c2 ~ e^-1|\log\varepsilon|\ll\varOmega< \varOmega_{\mathrm{c_{2}}}\sim \varepsilon^{-1} the vorticity is uniformly distributed over the disc. For \varOmega 3 \varOmega _c2\varOmega\geq\varOmega _{\mathrm{c_{2}}} the centrifugal forces create a hole around the center with strongly depleted density. For Ω≪ε ⁻²|log ε|⁻¹ vorticity is still uniformly distributed in an annulus containing the bulk of the density, but at \varOmega = \varOmega_c3 ~ e^-2|loge|^-1\varOmega=\varOmega_{\mathrm {c_{3}}}\sim\varepsilon ^{-2}|\log\varepsilon |^{-1} there is a transition to a giant vortex state where the vorticity disappears from the bulk. The energy is then well approximated by a trial function that is an eigenfunction of angular momentum but one of our results is that the true minimizers break rotational symmetry in the whole parameter range, including the giant vortex phase.     

On the Massive Wave Equation on Slowly Rotating Kerr-AdS Spacetimes

The massive wave equation ${\square_{g}\psi - \alpha \frac{\Lambda}{3}\psi = 0}The massive wave equation \square_gy- a\fracL3y = 0{\square_{g}\psi - \alpha \frac{\Lambda}{3}\psi = 0} is studied on a fixed Kerr-anti de Sitter background (M,g_M,a,L){\left(\mathcal{M},g_{M,a,\Lambda}\right)}. We first prove that in the Schwarzschild case (a = 0), ψ remains uniformly bounded on the black hole exterior provided that a < \frac94{\alpha < \frac{9}{4}}, i.e. the Breitenlohner-Freedman bound holds. Our proof is based on vectorfield multipliers and commutators: The total flux of the usual energy current arising from the timelike Killing vector field T (which fails to be non-negative pointwise) is shown to be non-negative with the help of a Hardy inequality after integration over a spacelike slice. In addition to T, we construct a vectorfield whose energy identity captures the redshift producing good estimates close to the horizon. The argument is finally generalized to slowly rotating Kerr-AdS backgrounds. This is achieved by replacing the Killing vectorfield T = ∂ _t with K=?_t + l?_f{K=\partial_t + \lambda \partial_\phi} for an appropriate λ ~ a, which is also Killing and–in contrast to the asymptotically flat case–everywhere causal on the black hole exterior. The separability properties of the wave equation on Kerr-AdS are not used. As a consequence, the theorem also applies to spacetimes sufficiently close to the Kerr-AdS spacetime, as long as they admit a causal Killing field K which is null on the horizon.     

Higher Dimensional Bianchi Type-V Cosmological Models with Perfect Fluid and Dark Energy

We have studied the Bianchi type-V cosmological models with binary mixture of perfect fluid and dark energy in five dimensions. The perfect fluid is obeying the equation of state p=γρ with γ∈[0,1]. The dark energy is considered to be either the quintessence or the Chaplygin gas. The exact solutions of the Einstein’s field equations are obtained in quadrature form.     

Cosmology with a variable generalized Chaplygin gas

We investigate observational constraint on the variable generalized Chaplygin gas (VGCG) model as the unification of dark matter and dark energy by using the Union supernovae sample and the baryon acoustic oscillations data. Based on the best fit parameters for VGCG model it is shown that the current value of equation of state for dark energy is w_0de=−1.08<−1, and the universe will not end up with big rip in the future. In addition, we also discuss the evolution of several quantities in VGCG cosmology such as deceleration parameter, fractional density parameters, growth index and sound speed. Finally, the statefinder diagnostic is performed to discriminate the VGCG with other models.     

On parity-violating three-nucleon interactions and the predictive power of few-nucleon EFT at very low energies

We address the typical strengths of hadronic parity-violating three-nucleon interactions in “pion-less” Effective Field Theory (EFT) in the nucleon-deuteron (iso-doublet) system. By analysing the superficial degree of divergence of loop diagrams, we conclude that no such interactions are needed at leading order, O(eQ^-1)\ensuremath {O}(\epsilon Q^{-1}) . The only two distinct parity-violating three-nucleon structures with one derivative mix ²S_\frac12\ensuremath ^2S_{\frac{1}{2}} and ²P_\frac12\ensuremath ^2P_{\frac{1}{2}} waves with iso-spin transitions D \Delta I = 0 or 1. Due to their structure, they cannot absorb any divergence ostensibly appearing at next-to-leading order, O(eQ⁰)\ensuremath {O}(\epsilon Q^0) . This observation is based on the approximate realisation of Wigner’s combined SU(4) spin-isospin symmetry in the two-nucleon system, even when effective-range corrections are included. Parity-violating three-nucleon interactions thus only appear beyond next-to-leading order. This guarantees renormalisability of the theory to that order without introducing new, unknown coupling constants and allows the direct extraction of parity-violating two-nucleon interactions from three-nucleon experiments.     

Invariance of the White Noise for KdV

We prove the invariance of the mean 0 white noise for the periodic KdV. First, we show that the Besov-type space [^(b)]^s_p,￥{\widehat{b}^s_{p,\infty}} , sp < −1, contains the support of the white noise. Then, we prove local well-posedness in [^(b)]^s_{p, ￥}{\widehat{b}^s_{p, \infty}} for p = 2 + , s = -\frac12+{s = -\frac{1}{2}+} such that sp < −1. In establishing the local well-posedness, we use a variant of the Bourgain spaces with a weight. This provides an analytical proof of the invariance of the white noise under the flow of KdV obtained in Quastel-Valko [21].