Stability analysis of cosmological models through Liapunov's method

We investigate the general asymptotic behaviour of Friedman-Robertson-Walker (FRW) models with an inflaton field, scalar-tensor FRW cosmological models and diagonal Bianchi-IX models by means of Liapunov's method. This method provides information not only about the asymptotic stability of a given equilibrium point but also about its basin of attraction. This cannot be obtained by the usual methods found in the literature, such as linear stability analysis or first order perturbation techniques. Moreover, Liapunov's method is also applicable to non-autonomous systems. We use this advantadge to investigate the mechanism of reheating for the inflaton field in FRW models.Comment: Latex file, 8 pages, no figures, accepted for publication in Class. & Quant. Gra

A Solution to the Graceful Exit Problem in Pre-Big Bang Cosmology

We examine the string cosmology equations with a dilaton potential in the context of the Pre-Big Bang Scenario with the desired scale factor duality, and give a generic algorithm for obtaining solutions with appropriate evolutionary properties. This enables us to find pre-big bang type solutions with suitable dilaton behaviour that are regular at $t=0$, thereby solving the graceful exit problem. However to avoid fine tuning of initial data, an `exotic' equation of state is needed that relates the fluid properties to the dilaton field. We discuss why such an equation of state should be required for reliable dilaton behaviour at late times.Comment: 16 pages LaTeX, 5 figures. To appear in Physical Review

Gravity Waves Signatures from Anisotropic pre-Inflation

We show that expanding or contracting Kasner universes are unstable due to the amplification of gravitational waves (GW). As an application of this general relativity effect, we consider a pre-inflationary anisotropic geometry characterized by a Kasner-like expansion, which is driven dynamically towards inflation by a scalar field. We investigate the evolution of linear metric fluctuations around this background, and calculate the amplification of the long-wavelength GW of a certain polarization during the anisotropic expansion (this effect is absent for another GW polarization, and for scalar fluctuations). These GW are superimposed to the usual tensor modes of quantum origin from inflation, and are potentially observable if the total number of inflationary e-folds exceeds the minimum required to homogenize the observable universe only by a small margin. Their contribution to the temperature anisotropy angular power spectrum decreases with the multipole l as l^(-p), where p depends on the slope of the initial GW power-spectrum. Constraints on the long-wavelength GW can be translated into limits on the total duration of inflation and the initial GW amplitude. The instability of classical GW (and zero-vacuum fluctuations of gravitons) during Kasner-like expansion (or contraction) may have other interesting applications. In particular, if GW become non-linear, they can significantly alter the geometry before the onset of inflation

Electrode Kinetics of Vanadium Flow Batteries: Contrasting Responses of V\u3csup\u3eII\u3c/sup\u3e-V\u3csup\u3eIII\u3c/sup\u3e and V\u3csup\u3eIV\u3c/sup\u3e-V\u3csup\u3eV\u3c/sup\u3e to Electrochemical Pretreatment of Carbon

Electrochemical impedance spectroscopy and cyclic voltammetry were used to investigate the electrode kinetics of VII-VIII and VIV-VV in H2SO4 on glassy carbon, carbon paper, carbon xerogel, and carbon fibers. It was shown that, for all carbon materials investigated, the kinetics of VII-VIII is enhanced by anodic, and inhibited by cathodic, treatment of the electrode; in contrast, the kinetics of VIV-VV is inhibited by anodic, and enhanced by cathodic, treatment. The potential region for each of these effects varied only slightly with carbon material. Rate constants were always greater for VIV-VV than for VII-VIII except when anodized electrodes were compared, which may explain discrepancies in the literature. The observed effects are attributed to oxygen-containing functional-groups on the electrode surface. The considerable differences between the potentials at which enhancement of VII-VIII and inhibition of VIV-VV occur indicates that they do not correspond to a common oxidized state of the electrode. Likewise inhibition of VII-VIII and enhancement of VIV-VV do not correspond to a common reduced state of the electrode. It is possible that enhancement of both VII-VIII and VIV-VV is due to the same (active) state of the electrode

Solution generating in scalar-tensor theories with a massless scalar field and stiff perfect fluid as a source

We present a method for generating solutions in some scalar-tensor theories with a minimally coupled massless scalar field or irrotational stiff perfect fluid as a source. The method is based on the group of symmetries of the dilaton-matter sector in the Einstein frame. In the case of Barker's theory the dilaton-matter sector possesses SU(2) group of symmetries. In the case of Brans-Dicke and the theory with "conformal coupling", the dilaton- matter sector has $SL(2,R)$ as a group of symmetries. We describe an explicit algorithm for generating exact scalar-tensor solutions from solutions of Einstein-minimally-coupled-scalar-field equations by employing the nonlinear action of the symmetry group of the dilaton-matter sector. In the general case, when the Einstein frame dilaton-matter sector may not possess nontrivial symmetries we also present a solution generating technique which allows us to construct exact scalar-tensor solutions starting with the solutions of Einstein-minimally-coupled-scalar-field equations. As an illustration of the general techniques, examples of explicit exact solutions are constructed. In particular, we construct inhomogeneous cosmological scalar-tensor solutions whose curvature invariants are everywhere regular in space-time. A generalization of the method for scalar-tensor-Maxwell gravity is outlined.Comment: 10 pages,Revtex; v2 extended version, new parts added and some parts rewritten, results presented more concisely, some simple examples of homogeneous solutions replaced with new regular inhomogeneous solutions, typos corrected, references and acknowledgements added, accepted for publication in Phys.Rev.

Bounce behaviour in Kantowski-Sachs and Bianchi Cosmologies

Many cosmological scenarios envisage either a bounce of the universe at early times, or collapse of matter locally to form a black hole which re-expands into a new expanding universe region. Energy conditions preclude this happening for ordinary matter in general relativistic universes, but scalar or dilatonic fields can violate some of these conditions, and so could possibly provide bounce behaviour. In this paper we show that such bounces cannot occur in Kantowski-Sachs models without violating the {\it reality condition} $\dot{\phi}^2\geq 0$. This also holds true for other isotropic spatially homogenous Bianchi models, with the exception of closed Friedmann-Robertson-Walker and Bianchi IX models; bounce behaviour violates the {\em weak energy condition} $\rho\geq 0$ and $\rho+p\geq 0$. We turn to the Randall-Sundrum type braneworld scenario for a possible resolution of this problem.Comment: Matches published versio

Evaluation of the West Yorkshire Staff Mental Health and Wellbeing Hub

The West Yorkshire (WY) Staff Wellbeing Hub aims to support NHS, Social Care and Voluntary Sector staff. This evaluation has been conducted as a partnership between the WY Hub and the University of Leeds. It presents data reflecting user uptake and experiences

Structure and stability of the Lukash plane-wave spacetime

We study the vacuum, plane-wave Bianchi $VII{}_{h}$ spacetimes described by the Lukash metric. Combining covariant with orthonormal frame techniques, we describe these models in terms of their irreducible kinematical and geometrical quantities. This covariant description is used to study analytically the response of the Lukash spacetime to linear perturbations. We find that the stability of the vacuum solution depends crucially on the background shear anisotropy. The stronger the deviation from the Hubble expansion, the more likely the overall linear instability of the model. Our analysis addresses rotational, shear and Weyl curvature perturbations and identifies conditions sufficient for the linear growth of these distortions.Comment: Revised version, references added. To appear in Class. Quantum Gra