arXiv subjects
Publications and source records attributed to Peter Dunsby.
The generation of gravitational waves during inflation due to the non-linear coupling of scalar and tensor modes is discussed. Two methods describing gravitational wave perturbations are used and compared: a covariant and local approach, as well as a metric-based analysis based on the Bardeen formalism. An application to slow-roll inflation is also described.
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} $\dotϕ^2\geq 0$. 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} $ρ\geq 0$ and $ρ+p\geq 0$. We turn to the Randall-Sundrum type braneworld scenario for a possible resolution of this problem.
Using second-order gauge-invariant perturbation theory, a self-consistent framework describing the non-linear coupling between gravitational waves and a large-scale homogeneous magnetic field is presented. It is shown how this coupling may be used to amplify seed magnetic fields to strengths needed to support the galactic dynamo. In situations where the gravitational wave background is described by an `almost' Friedmann-Lema{î}tre-Robertson-Walker (FLRW) cosmology we find that the magnitude of the original magnetic field is amplified by an amount proportional to the magnitude of the gravitational wave induced shear anisotropy and the square of the field's initial co-moving scale. We apply this mechanism to the case where the seed field and gravitational wave background are produced during inflation and find that the magnitude of the gravitational boost depends significantly on the manner in which the estimate of the shear anisotropy at the end of inflation is calculated. Assuming a seed field of $10^{-34}$ $\rm{G}$ spanning a comoving scale of about $10 \rm{kpc}$ today, the shear anisotropy at the end of inflation must be at least as large as $10^{-40}$ in order to obtain a generated magnetic field of the same order of magnitude as the original seed. Moreover, contrasting the weak field approximation to our gauge-invariant approach, we find that while both methods agree in the limit of high conductivity, their corresponding solutions are otherwise only compatible in the limit of infinitely long-wavelength gravitational waves.
In this work we consider Randall-Sundrum braneworld type scenarios, in which the spacetime is described by a five-dimensional manifold with matter fields confined in a domain wall or three-brane. We present the results of a systematic analysis, using dynamical systems techniques, of the qualitative behaviour of Friedmann-Lemaitre-Robertson-Walker type models, whose matter is described by a scalar field with an exponential potential. We construct the state spaces for these models and discuss how their structure changes with respect to the general-relativistic case, in particular, what new critical points appear and their nature and the occurrence of bifurcation.
We discuss the dynamics of linear, scalar perturbations in an almost Friedmann-Robertson-Walker braneworld cosmology of Randall-Sundrum type II using the 1+3 covariant approach. We derive a complete set of frame-independent equations for the total matter variables, and a partial set of equations for the non-local variables which arise from the projection of the Weyl tensor in the bulk. The latter equations are incomplete since there is no propagation equation for the non-local anisotropic stress. We supplement the equations for the total matter variables with equations for the independent constituents in a cold dark matter cosmology, and provide solutions in the high and low-energy radiation-dominated phase under the assumption that the non-local anisotropic stress vanishes. These solutions reveal the existence of new modes arising from the two additional non-local degrees of freedom. Our solutions should prove useful in setting up initial conditions for numerical codes aimed at exploring the effect of braneworld corrections on the cosmic microwave background (CMB) power spectrum. As a first step in this direction, we derive the covariant form of the line of sight solution for the CMB temperature anisotropies in braneworld cosmologies, and discuss possible mechanisms by which braneworld effects may remain in the low-energy universe.
A general system of equations is derived, using the 1+3 orthonormal tetrad formalism, describing the influence of a plane-fronted-parallel gravitational wave on a warm relativistic two-component plasma. We focus our attention on phenomena that are induced by terms that are higher order in the gravitational wave amplitude. In particular, it is shown that parametric excitations of ion-acoustic waves takes place, due to these higher order gravitational non-linearities. The implications of the results are discussed.
In Randall-Sundrum type braneworld cosmologies, the dynamical equations on the three-brane differ from the general relativity equations by terms that carry the effects of embedding and of the free gravitational field in the five-dimensional bulk. In a FRW ansatze for the metric, we present two methods for deriving inflationary solutions to the covariant non-linear dynamical equations for the gravitational and matter fields on the brane. In the first approach we examine the constraints on the dynamical relationship between the cosmological scale factor and the scalar field driving self-interaction potential, imposed by the weak energy condition. We then investigate inflationary solutions obtained from a scalar field superpotential. Both these techniques for solving the braneworld field equations are illustrated by flat curvature models.
We consider the interaction of a weak gravitational wave with electromagnetic fields in a thin plasma on a Minkowski background spacetime using the 1+3 orthonormal frame formalism. Because gravitational and electromagnetic waves satisfy the same dispersion relation, electromagnetic waves can be effectively generated as a result of this interaction. In the case of the interaction with a static magnetic field, the amplitude of the electromagnetic waves depends on the size of the excitation region in which the magnetic field is contained. It is argued that due to the presence of a plasma this process can also lead to the generation of higher harmonics of the original mode. Estimates are given for this effect in the case of a binary pulsar and a cold electron plasma. It is found that the emmited radiation will lie in the radio frequency band. We also speculate on the possible relevance of this process on situations in cosmology, in particular whether this could be used to constrain primordial magnetic fields.
This is the second of a series of papers extending the 1+3 covariant and gauge invariant treatment of kinetic theory to an examination of Cosmic Microwave Background temperature anisotropies arising from inhomogeneities in the early universe. The first paper dealt with algebraic issues. Here we derive the mode form of the integrated Boltzmann equations, first, giving a covariant version of the standard derivation using the mode recursion relations, second, demonstrating the link to the multipole divergence equations and finally various analytic ways of solving the resulting equations are discussed. A general integral form of solution is obtained for the equations with Thomson scattering. The covariant Friedmann-Lemaitre multipole form of the transport equations are found using the covariant and gauge-invariant generalization of the Peebles and Yu expansion in Thompson scattering time. The dispersion relations and damping scale are then obtained from the covariant approach. The equations are integrated to give the covariant and gauge-invariant equivalent of the canonical scalar sourced anisotropies. We carry out a simple treatment of the matter dominated free-streaming projection, slow decoupling, and tight-coupling cases, with the aim both giving a unified transparent derivation of this range of results and clarifying the connection between the more usual approaches (for example that of Hu and Sugiyama) and the treatment for scalar perturbations (for example the treatment of Challinor and Lasenby).
The propagation of gravitational waves or tensor perturbations in a perturbed Friedmann-Robertson-Walker universe filled with a perfect fluid is re-examined. It is shown that while the shear and magnetic part of the Weyl tensor satisfy linear, homogeneous {\it second order} wave equations, for perfect fluids with a $γ$\hs law equation of state satisfying $\case{2}/{3}<γ<2$, the electric part of the Weyl tensor satisfies a linear homogeneous {\it third order} equation. Solutions to these equations are obtained for a flat Friedmann-Robertson-Walker background and we discuss implications of this result.
Inflationary models and their claim to solve many of the outstanding problems in cosmology have been the subject of a great deal of debate over the last few years. A major sticking point has been the lack of both good observational and theoretical arguments to single out one particular model out of the many that solve these problems. Here we examine the degree of restrictiveness on the dynamical relationship between the cosmological scale factor and the inflation driving self-interaction potential of a minimally coupled scalar field, imposed by the condition that the scalar field is required to be real during a classical regime (the reality condition). We systema\-tically look at the effects of this constraint on many of the inflationary models found in the literature within the FLRW framework, and also look at what happens when physically motivated perturbations such as shear and bulk viscosity are introduced. We find that in many cases, either the models are totally excluded or the reality condition gives rise to constraints on the scale factor and on the various parameters of the model.
Given that observations seem to favour a \index{density parameter} $Ω_0<1$, corresponding to an open universe, we consider gauge\hs invariant perturbations of non\hs flat Robertson\hs Walker universes filled with a general imperfect fluid which can also be taken to represent a scalar field. Our aim is to set up the equations that govern the evolution of the density perturbations $Δ$ so that it can be determined through a {\it first order differential equation} with a quantity $\kk$ which is conserved at any length scale, even in non\hs flat universe models, acting as a source term. The quantity $\kk$ generalizes other variables that are conserved in specific cases (for example at large scales in a flat universe) and is useful to connect different epochs in the evolution of density perturbations via a transfer function. We show that the problem of finding a conserved $\kk$ can be reduced to determining two auxiliary variables $X$ and $Y$, and illustrate the method with two simple examples.