Scalar field in cosmology: Potential for isotropization and inflation

The important role of scalar field in cosmology was noticed by a number of authors. Due to the fact that the scalar field possesses zero spin, it was basically considered in isotropic cosmological models. If considered in an anisotropic model, the linear scalar field does not lead to isotropization of expansion process. One needs to introduce scalar field with nonlinear potential for the isotropization process to take place. In this paper the general form of scalar field potentials leading to the asymptotic isotropization in case of Bianchi type-I cosmological model, and inflationary regime in case of isotropic space-time is obtained. In doing so we solved both direct and inverse problem, where by direct problem we mean to find metric functions and scalar field for the given potential, whereas, the inverse problem means to find the potential and scalar field for the given metric function. The scalar field potentials leading to the inflation and isotropization were found both for harmonic and proper synchronic time.Comment: 10 page

Developing the MTO Formalism

We review the simple linear muffin-tin orbital method in the atomic-spheres approximation and a tight-binding representation (TB-LMTO-ASA method), and show how it can be generalized to an accurate and robust Nth order muffin-tin orbital (NMTO) method without increasing the size of the basis set and without complicating the formalism. On the contrary, downfolding is now more efficient and the formalism is simpler and closer to that of screened multiple-scattering theory. The NMTO method allows one to solve the single-electron Schroedinger equation for a MT-potential -in which the MT-wells may overlap- using basis sets which are arbitrarily minimal. The substantial increase in accuracy over the LMTO-ASA method is achieved by substitution of the energy-dependent partial waves by so-called kinked partial waves, which have tails attached to them, and by using these kinked partial waves at N+1 arbitrary energies to construct the set of NMTOs. For N=1 and the two energies chosen infinitesimally close, the NMTOs are simply the 3rd-generation LMTOs. Increasing N, widens the energy window, inside which accurate results are obtained, and increases the range of the orbitals, but it does not increase the size of the basis set and therefore does not change the number of bands obtained. The price for reducing the size of the basis set through downfolding, is a reduction in the number of bands accounted for and -unless N is increased- a narrowing of the energy window inside which these bands are accurate. A method for obtaining orthonormal NMTO sets is given and several applications are presented.Comment: 85 pages, Latex2e, Springer style, to be published in: Lecture notes in Physics, edited by H. Dreysse, (Springer Verlag

Interacting spinor and scalar fields in Bianchi type-I Universe filled with viscous fluid: exact and numerical solutions

We consider a self-consistent system of spinor and scalar fields within the framework of a Bianchi type I gravitational field filled with viscous fluid in presence of a $\Lambda$ term. Exact self-consistent solutions to the corresponding spinor, scalar and BI gravitational field equations are obtained in terms of $\tau$, where $\tau$ is the volume scale of BI universe. System of equations for $\tau$ and \ve, where \ve is the energy of the viscous fluid, is deduced. Some special cases allowing exact solutions are thoroughly studied.Comment: 18 pages, 6 figure

Third-Generation TB-LMTO

We describe the screened Korringa-Kohn-Rostoker (KKR) method and the third-generation linear muffin-tin orbital (LMTO) method for solving the single-particle Schroedinger equation for a MT potential. The simple and popular formalism which previously resulted from the atomic-spheres approximation (ASA) now holds in general, that is, it includes downfolding and the combined correction. Downfolding to few-orbital, possibly short-ranged, low-energy, and possibly orthonormal Hamiltonians now works exceedingly well, as is demonstrated for a high-temperature superconductor. First-principles sp3 and sp3d5 TB Hamiltonians for the valence and lowest conduction bands of silicon are derived. Finally, we prove that the new method treats overlap of the potential wells correctly to leading order and we demonstrate how this can be exploited to get rid of the empty spheres in the diamond structure.Comment: latex2e, 32 printed pages, Postscript figs, to be published in: Tight-Binding Approach to Computational Materials Science, MRS Symposia Proceedings No. 491 (MRS, Pittsburgh, 1998

Gauge invariances vis-{\'a}-vis Diffeomorphisms in second order metric gravity: A new Hamiltonian approach

A new analysis of the gauge invariances and their unity with diffeomorphism invariances in second order metric gravity is presented which strictly follows Dirac's constrained Hamiltonian approach.Comment: 6 Pages, revTex, paper modified substantiall

COSMOGRAIL: the COSmological MOnitoring of GRAvItational Lenses VII. Time delays and the Hubble constant from WFI J2033-4723

Gravitationally lensed quasars can be used to map the mass distribution in lensing galaxies and to estimate the Hubble constant H0 by measuring the time delays between the quasar images. Here we report the measurement of two independent time delays in the quadruply imaged quasar WFI J2033-4723 (z = 1.66). Our data consist of R-band images obtained with the Swiss 1.2 m EULER telescope located at La Silla and with the 1.3 m SMARTS telescope located at Cerro Tololo. The light curves have 218 independent epochs spanning 3 full years of monitoring between March 2004 and May 2007, with a mean temporal sampling of one observation every 4th day. We measure the time delays using three different techniques, and we obtain Dt(B-A) = 35.5 +- 1.4 days (3.8%) and Dt(B-C) = 62.6 +4.1/-2.3 days (+6.5%/-3.7%), where A is a composite of the close, merging image pair. After correcting for the time delays, we find R-band flux ratios of F_A/F_B = 2.88 +- 0.04, F_A/F_C = 3.38 +- 0.06, and F_A1/F_A2 = 1.37 +- 0.05 with no evidence for microlensing variability over a time scale of three years. However, these flux ratios do not agree with those measured in the quasar emission lines, suggesting that longer term microlensing is present. Our estimate of H0 agrees with the concordance value: non-parametric modeling of the lensing galaxy predicts H0 = 67 +13/-10 km s-1 Mpc-1, while the Single Isothermal Sphere model yields H0 = 63 +7/-3 km s-1 Mpc-1 (68% confidence level). More complex lens models using a composite de Vaucouleurs plus NFW galaxy mass profile show twisting of the mass isocontours in the lensing galaxy, as do the non-parametric models. As all models also require a significant external shear, this suggests that the lens is a member of the group of galaxies seen in field of view of WFI J2033-4723.Comment: 14 pages, 12 figures, published in A&

Pulsive feedback control for stabilizing unstable periodic orbits in a nonlinear oscillator with a non-symmetric potential

We examine a strange chaotic attractor and its unstable periodic orbits in case of one degree of freedom nonlinear oscillator with non symmetric potential. We propose an efficient method of chaos control stabilizing these orbits by a pulsive feedback technique. Discrete set of pulses enable us to transfer the system from one periodic state to another.Comment: 11 pages, 4 figure