Covariant Formulation of the Invariant Measure for the Mixmaster Dynamics

We provide a Hamiltonian analysis of the Mixmaster Universe dynamics showing the covariant nature of its chaotic behavior with respect to any choice of time variable. We construct the appropriate invariant measure for the system (which relies on the existence of an ``energy-like'' constant of motion) without fixing the time gauge, i.e. the corresponding lapse function. The key point in our analysis consists of introducing generic Misner-Chitr\'e-like variables containing an arbitrary function, whose specification allows one to set up the same dynamical scheme in any time gauge.Comment: 11 pages, 1 figur

Cosmological Acceleration from Virtual Gravitons

Intrinsic properties of the space itself and quantum fluctuations of its geometry are sufficient to provide a mechanism for the acceleration of cosmological expansion (dark energy effect). Applying Bogoliubov-Born-Green-Kirkwood-Yvon hierarchy approach to self-consistent equations of one-loop quantum gravity, we found exact solutions that yield acceleration. The permanent creation and annihilation of virtual gravitons is not in exact balance because of the expansion of the Universe. The excess energy comes from the spontaneous process of graviton creation and is trapped by the background. It provides the macroscopic quantum effect of cosmic acceleration.Comment: 6 pages, REVTeX

Universe from vacuum in loop-string cosmology

In this paper we study the description of the Universe based on the low energy superstring theory modified by the Loop Quantum Gravity effects.This approach was proposed by De Risi et al. in the Phys. Rev. D {\bf 76} (2007) 103531. We show that in the contrast with the string motivated pre-Big Bang scenario, the cosmological realisation of the $t$-duality transformation is not necessary to avoid an initial singularity. In the model considered the universe starts its evolution in the vacuum phase at time $t\to - \infty$. In this phase the scale factor $a\to 0$, energy density $\rho \to 0$ and coupling of the interactions $g^2_s \to 0$. After this stage the universe evolves to the non-singular hot Big Bang phase $\rho \to \rho_{\text{max}} < \infty$. Then the standard classical universe emerges. During the whole evolution the scale factor increases monotonically. We solve this model analytically. We also propose and solve numerically the model with an additional dilaton potential in which the universe starts the evolution from the asymptotically free vacuum phase $g^2_s \to 0$ and then evolves non-singularly to the emerging dark energy dominated phase with the saturated coupling constant $g^2_s \to \text{const}$.Comment: JHEP3 LaTeX class, 19 pages, 9 figures, v2: added some comments and references, v3: new numerical result added, new figure

Geometry of dynamics, Lyapunov exponents and phase transitions

The Hamiltonian dynamics of classical planar Heisenberg model is numerically investigated in two and three dimensions. By considering the dynamics as a geodesic flow on a suitable Riemannian manifold, it is possible to analytically estimate the largest Lyapunov exponent in terms of some curvature fluctuations. The agreement between numerical and analytical values for Lyapunov exponents is very good in a wide range of temperatures. Moreover, in the three dimensional case, in correspondence with the second order phase transition, the curvature fluctuations exibit a singular behaviour which is reproduced in an abstract geometric model suggesting that the phase transition might correspond to a change in the topology of the manifold whose geodesics are the motions of the system.Comment: REVTeX, 10 pages, 5 PostScript figures, published versio

Overlapping functions of the starch synthases SSII and SSIII in amylopectin biosynthesis in Arabidopsis

Background: The biochemical mechanisms that determine the molecular architecture of amylopectin are central in plant biology because they allow long-term storage of reduced carbon. Amylopectin structure imparts the ability to form semi-crystalline starch granules, which in turn provides its glucose storage function. The enzymatic steps of amylopectin biosynthesis resemble those of the soluble polymer glycogen, however, the reasons for amylopectin's architectural distinctions are not clearly understood. The multiplicity of starch biosynthetic enzymes conserved in plants likely is involved. For example, amylopectin chain elongation in plants involves five conserved classes of starch synthase (SS), whereas glycogen biosynthesis typically requires only one class of glycogen synthase. Results: Null mutations were characterized in AtSS2, which codes for SSII, and mutant lines were compared to lines lacking SSIII and to an Atss2, Atss3 double mutant. Loss of SSII did not affect growth rate or starch quantity, but caused increased amylose/amylopectin ratio, increased total amylose, and deficiency in amylopectin chains with degree of polymerization (DP) 12 to DP28. In contrast, loss of both SSII and SSIII caused slower plant growth and dramatically reduced starch content. Extreme deficiency in DP12 to DP28 chains occurred in the double mutant, far more severe than the summed changes in SSII- or SSIII-deficient plants lacking only one of the two enzymes. Conclusion: SSII and SSIII have partially redundant functions in determination of amylopectin structure, and these roles cannot be substituted by any other conserved SS, specifically SSI, GBSSI, or SSIV. Even though SSIII is not required for the normal abundance of glucan chains of DP12 to DP18, the enzyme clearly is capable of functioning in production such chains. The role of SSIII in producing these chains cannot be detected simply by analysis of an individual mutation. Competition between different SSs for binding to substrate could in part explain the specific distribution of glucan chains within amylopectin

Observational Constraints on the Generalized Chaplygin Gas

In this paper we study a quintessence cosmological model in which the dark energy component is considered to be the Generalized Chaplygin Gas and the curvature of the three-geometry is taken into account. Two parameters characterize this sort of fluid, the $\nu$ and the $\alpha$ parameters. We use different astronomical data for restricting these parameters. It is shown that the constraint $\nu \lesssim \alpha$ agrees enough well with the astronomical observations.Comment: Accepted by IJMPD; 18 pages; 10 Figure

Constraints on alternative models to dark energy

The recent observations of type Ia supernovae strongly support that the universe is accelerating now and decelerated in the recent past. This may be the evidence of the breakdown of the standard Friemann equation. We consider a general modified Friedmann equation. Three different models are analyzed in detail. The current supernovae data and the Wilkinson microwave anisotropy probe data are used to constrain these models. A detailed analysis of the transition from the deceleration phase to the acceleration phase is also performed.Comment: 10 pages, 1 figure, revtex

Stabilization of the Yang-Mills chaos in non-Abelian Born-Infeld theory

We investigate dynamics of the homogeneous time-dependent SU(2) Yang-Mills fields governed by the non-Abelian Born-Infeld lagrangian which arises in superstring theory as a result of summation of all orders in the string slope parameter $\alpha'$. It is shown that generically the Born-Infeld dynamics is less chaotic than that in the ordinary Yang-Mills theory, and at high enough field strength the Yang-Mills chaos is stabilized. More generally, a smothering effect of the string non-locality on behavior of classical fields is conjectured.Comment: 7 pages, 5 figure

(Non)Invariance of dynamical quantities for orbit equivalent flows

We study how dynamical quantities such as Lyapunov exponents, metric entropy, topological pressure, recurrence rates, and dimension-like characteristics change under a time reparameterization of a dynamical system. These quantities are shown to either remain invariant, transform according to a multiplicative factor or transform through a convoluted dependence that may take the form of an integral over the initial local values. We discuss the significance of these results for the apparent non-invariance of chaos in general relativity and explore applications to the synchronization of equilibrium states and the elimination of expansions

Fomin's conception of quantum cosmogenesis

The main aim of this paper is to extend the early approach to quantum cosmogenesis provided by Fomin. His approach was developed independently to the well-known Tryon description of the creation of the closed universe as a process of quantum fluctuation of vacuum. We apply the Fomin concept to derive the cosmological observables. We argue that Fomin's idea from his 1973 work, in contrast to Tryon's one has impact on the current Universe models and the proposed extension of his theory now can be tested by distant supernovae SNIa. Fomin's idea of the creation of the Universe is based on the intersection of two fundamental theories: general relativity and quantum field theory with the contemporary cosmological models with dark energy. As a result of comparison with contemporary approaches concerning dark energy, we found out that Fomin's idea appears in the context of the present acceleration of the Universe explanation: cosmological models with decaying vacuum. Contemporary it appears in the form of Ricci scalar dark energy connected with the holographic principle. We show also that the Fomin model admits the bounce instead of the initial singularity. We demonstrate that the Fomin model of cosmogenesis can be falsified and using SNIa data the values of model parameters is in agreement with observations.Comment: 12 pages, 4 figures; (v2) 22 pages, references added, figures improved; (v3) rewritten using revtex4; (v4) minor changes; (v5) improved formulas and extended statistical analysi