arXiv subjects

Richard Battye

Publications and source records attributed to Richard Battye.

At least 55 records · Page 3Linked to original sources

arXiv2009

Constraints on the anisotropy of dark energy

If the equation of state of dark energy is anisotropic there will be additional quadrupole anisotropy in the cosmic microwave background induced by the time dependent anisotropic stress quantified in terms of $Δw$. Assuming that the entire amplitude of the observed quadrupole is due to this anisotropy, we conservatively impose a limit of $|Δw| < 2.1\times 10^{-4}$ for any value of $w\ge -1$ assuming that $Ω_{\rm m}<0.5$. This is considerably tighter than that which comes from SNe. Stronger limits, upto a factor of 10, are possible for specific values of $Ω_{\rm m}$ and $w$. Since we assume this component is uncorrelated with the stochastic component from inflation, we find that both the expectation value and the sample variance are increased. There no improvement in the likelihood of an anomalously low quadrupole as suggested by previous work on an elliptical universe.

astro-ph.CO↗

arXiv2009

Stability and the equation of state for kinky vortons

Vortons are closed loops of superconducting strings carrying current and charge. A formalism has been developed to study vortons in terms of an elastic string approximation, but its implementation requires knowledge of the unknown equation of state, relating the string tension to the energy per unit length. Recently, a planar analogue of the vorton, known as a kinky vorton, has been introduced. In this paper we derive an exact formula for the equation of state of a kinky vorton and use it to calculate the properties of the associated elastic string, such as the transverse and longitudinal propagation speeds. In particular, the elastic string approximation predicts a complicated and highly non-trivial pattern of intervals of instability, which we are able to confirm using full field simulations. The implications of the results for vortons are also discussed.

hep-th↗

arXiv2009

Anisotropic dark energy and CMB anomalies

We investigate the breaking of global statistical isotropy caused by a dark energy component with an energy-momentum tensor which has point symmetry, that could represent a cubic or hexagonal crystalline lattice. In such models Gaussian, adiabatic initial conditions created during inflation can lead to anisotropies in the cosmic microwave background whose spherical harmonic coefficients are correlated, contrary to the standard assumption. We develop an adaptation of the line of sight integration method that can be applied to models where the background energy-momentum tensor is isotropic, but whose linearized perturbations are anisotropic. We then show how this can be applied to the cases of cubic and hexagonal symmetry. We compute quantities which show that such models are indistinguishable from isotropic models even in the most extreme parameter choices, in stark contrast to models with anisotropic initial conditions based on inflation. The reason for this is that the dark energy based models contribute to the CMB anistropy via the inegrated Sachs-Wolfe effect, which is only relevent when the dark energy is dominant, that is, on the very largest scales. For inflationary models, however, the anisotropy is present on all scales.

astro-ph.CO↗

arXiv2008

Vorton construction and dynamics

Vortons are closed loops of superconducting cosmic strings carrying current and charge. In this paper we present the first numerical construction of vortons in the global version of Witten's U(1)xU(1) theory. An energy minimization procedure is used to compute stationary vortons for a range of charges and currents, and the associated vorton radius is calculated. It is found that the standard analysis based on infinite straight cosmic strings does not provide a good description of the vorton cross-section. The computed solutions are used as initial conditions in an axially symmetric time evolution code, which verifies that the solutions are indeed stationary, and are stable to axially symmetric perturbations. Perturbations which preserve the axial symmetry excite oscillatory modes and produce an evolution which eventually returns to a stationary vorton. Finally, the constructed vorton solutions are used as initial conditions in a full (3+1)-dimensional simulation and an instability to non-axial perturbations is found. The instability produces a pinching and bending of the vorton which results in its destruction.

hep-th↗

arXiv2008

Kinky Vortons

Cosmic vortons are closed loops of superconducting cosmic strings carrying current and charge. Despite a large number of studies the existence and stability of cosmic vorton solutions is still an open problem. Numerical simulations of the nonlinear field theory are difficult to perform in (3+1)-dimensions, due to the existence of multiple length and time scales. In this paper we study a (2+1)-dimensional analogue of cosmic vortons, which we refer to as kinky vortons, where the cosmic string is replaced by a kink string. Many of the expected qualitative aspects of cosmic vortons transfer to kinky vortons, with the advantage that several approximations used in the study of cosmic vortons can be replaced by exact results. Furthermore, the numerical study of kinky vortons requires less computational resources than cosmic vortons, so a number of issues can be addressed in some depth. The radius of the kinky vorton is determined as a function of the charge and winding number, and it is shown that the chiral limit is a repulsive fixed point. Stability to both axial and non-axial perturbations is demonstrated in the electric and chiral regimes, though surprisingly long lived ringing modes are observed. Kinky vortons which are too magnetic are shown to suffer from a pinching instability, which results in a reduction in the winding number and can convert magnetic into electric solutions.

hep-th↗

arXiv2006

The Cosmic Microwave Background and the Ionization History of the Universe

Details of how the primordial plasma recombined and how the universe later reionized are currently somewhat uncertain. This uncertainty can restrict the accuracy of cosmological parameter measurements from the Cosmic Microwave Background (CMB). More positively, future CMB data can be used to constrain the ionization history using observations. We first discuss how current uncertainties in the recombination history impact parameter constraints, and show how suitable parameterizations can be used to obtain unbiased parameter estimates from future data. Some parameters can be constrained robustly, however there is clear motivation to model recombination more accurately with quantified errors. We then discuss constraints on the ionization fraction binned in redshift during reionization. Perfect CMB polarization data could in principle distinguish different histories that have the same optical depth. We discuss how well the Planck satellite may be able to constrain the ionization history, and show the currently very weak constraints from WMAP three-year data.

astro-ph↗

arXiv2006

Skyrmions and the alpha-particle model of nuclei

We compute new solutions of the Skyrme model with massive pions. Concentrating on baryon numbers which are a multiple of four, we find low energy Skyrmion solutions which are composed of charge four sub-units, as in the alpha-particle model of nuclei. We summarize our current understanding of these solutions, and discuss their relationship to configurations in the alpha-particle model.

hep-th↗

arXiv2006

Skyrmions with massive pions

In the Skyrme model with massless pions, the minimal energy multi-Skyrmions are shell-like, with the baryon density localized on the edges of a polyhedron that is approximately spherical and generically of the fullerene-type. In this paper we show that in the Skyrme model with massive pions these configurations are unstable for sufficiently large baryon number. Using numerical simulations of the full nonlinear field theory, we show that these structures collapse to form qualitatively different stable Skyrmion solutions. These new Skyrmions have a flat structure and display a clustering phenomenon into lower charge components, particularly components of baryon numbers three and four. These new qualitative features of Skyrmions with massive pions are encouraging in comparison with the expectations based on real nuclei.

hep-th↗

arXiv2004

Skyrmions and the pion mass

We present numerical evidence that suggests the introduction of a non-zero pion mass might dramatically affect the structure of minimal energy Skyrmions. It appears that the shell-like Skyrmions which are the minima when the pions are massless can fail to be minimal energy bound states for particular baryon numbers, with a strong dependence upon the value of the pion mass. The effects of a pion mass may include the replacement of shell-like configurations with crystal chunks and the loss of shell-like bound states with baryon numbers five and eight; which is in agreement with expectations based on real nuclei.

hep-ph↗

arXiv2002

Polyhedral Scattering of Fundamental Monopoles

The dynamics of n slowly moving fundamental monopoles in the SU(n+1) BPS Yang-Mills-Higgs theory can be approximated by geodesic motion on the 4n-dimensional hyperkahler Lee-Weinberg-Yi manifold. In this paper we apply a variational method to construct some scaling geodesics on this manifold. These geodesics describe the scattering of n monopoles which lie on the vertices of a bouncing polyhedron; the polyhedron contracts from infinity to a point, representing the spherically symmetric n-monopole, and then expands back out to infinity. For different monopole masses the solutions generalize to form bouncing nested polyhedra. The relevance of these results to the dynamics of well separated SU(2) monopoles is also discussed.

hep-th↗

arXiv2002

Icosahedral Skyrmions

In this paper we aim to determine the baryon numbers at which the minimal energy Skyrmion has icosahedral symmetry. By comparing polyhedra which arise as minimal energy Skyrmions with the dual of polyhedra that minimize the energy of Coulomb charges on a sphere, we are led to conjecture a sequence of magic baryon numbers, B=7,17,37,67,97,... at which the minimal energy Skyrmion has icosahedral symmetry and unusually low energy. We present evidence for this conjecture by applying a simulated annealing algorithm to compute energy minimizing rational maps for all degrees upto 40. Further evidence is provided by the explicit construction of icosahedrally symmetric rational maps of degrees 37, 47, 67 and 97. To calculate these maps we introduce two new methods for computing rational maps with Platonic symmetries.

hep-th↗

arXiv2002

Central Configurations in Three Dimensions

We consider the equilibria of point particles under the action of two body central forces in which there are both repulsive and attractive interactions, often known as central configurations, with diverse applications in physics, in particular as homothetic time-dependent solutions to Newton's equations of motion and as stationary states in the One Component Plasma model. Concentrating mainly on the case of an inverse square law balanced by a linear force, we compute numerically equilibria and their statistical properties. When all the masses (or charges) of the particles are equal, for small numbers of points they are regular convex deltahedra, which on increasing the number of points give way to a multi-shell structure. In the limit of a large number of points we argue using an analytic model that they form a homogeneous spherical distribution of points, whose spatial distribution appears, from our preliminary investigation, to be similar to that of a Bernal hard-sphere liquid.

hep-th↗

arXiv2002

Constraining dark energy with Sunyaev-Zel'dovich cluster surveys

We discuss the prospects of constraining the properties of a dark energy component, with particular reference to a time varying equation of state, using future cluster surveys selected by their Sunyaev-Zel'dovich effect. We compute the number of clusters expected for a given set of cosmological parameters and propogate the errors expected from a variety of surveys. In the short term they will constrain dark energy in conjunction with future observations of type Ia supernovae, but may in time do so in their own right.

astro-ph↗

arXiv2001

Skyrmions, Fullerenes and Rational Maps

We apply two very different approaches to calculate Skyrmions with baryon number B less than 23. The first employs the rational map ansatz, where approximate charge B Skyrmions are constructed from a degree B rational map between Riemann spheres. We use a simulated annealing algorithm to search for the minimal energy rational map of a given degree B. The second involves the numerical solution of the full non-linear time dependent equations of motion, with initial conditions consisting of a number of well separated Skyrmion clusters. In general, we find a good agreement between the two approaches. For B greater than 6 almost all the solutions are of fullerene type, that is, the baryon density isosurface consists of twelve pentagons and 2B-14 hexagons arranged in a trivalent polyhedron. There are exceptional cases where this structure is modified, which we discuss in detail. We find that for a given value of B there are often many Skyrmions, with different symmetries, whose energies are very close to the minimal value, some of which we discuss. We present rational maps which are good approximations to these Skyrmions and accurately compute their energy by relaxation using the full non-linear dynamics.

hep-th↗

arXiv2000

Q-ball Dynamics

We investigate the dynamics of Q-balls in one, two and three space dimensions, using numerical simulations of the full nonlinear equations of motion. We find that the dynamics of Q-balls is extremely complex, involving processes such as charge transfer and Q-ball fission. We present results of simulations which illustrate the salient features of 2-Q-ball interactions and give qualitative arguments to explain them in terms of the evolution of the time-dependent phases.

hep-th↗

arXiv1998

Solitons, Links and Knots

Using numerical simulations of the full nonlinear equations of motion we investigate topological solitons of a modified O(3) sigma model in three space dimensions, in which the solitons are stabilized by the Hopf charge. We find that for solitons up to charge five the solutions have the structure of closed strings, which become increasingly twisted as the charge increases. However, for higher charge the solutions are more exotic and comprise linked loops and knots. We discuss the structure and formation of these solitons and demonstrate that the key property responsible for producing such a rich variety of solitons is that of string reconnection.

hep-th↗

arXiv1997

A Skyrme lattice with hexagonal symmetry

Recently it has been found that the structure of Skyrmions has a close analogy to that of fullerene shells in carbon chemistry. In this letter we show that this analogy continues further, by presenting a Skyrme field that describes a lattice of Skyrmions with hexagonal symmetry. This configuration, a novel `domain wall' in the Skyrme model, has low energy per baryon (about 6% above the Faddeev-Bogomolny bound) and in many ways is analogous to graphite. By comparison to the energy per baryon of other known Skyrmions and also the Skyrme crystal, we discuss the possibility of finding Skyrmion shells of higher charge.

hep-th↗

arXiv1997

Symmetric Skyrmions

We present candidates for the global minimum energy solitons of charge one to nine in the Skyrme model, generated using sophisticated numerical algorithms. Assuming the Skyrme model accurately represents the low energy limit of QCD, these configurations correspond to the classical nuclear ground states of the light elements. The solitons found are particularly symmetric, for example, the charge seven skyrmion has icosahedral symmetry, and the shapes are shown to fit a remarkable sequence defined by a geometric energy minimization (GEM) rule. We also calculate the energies and sizes to within at least a few percent accuracy. These calculations provide the basis for a future investigation of the low energy vibrational modes of skyrmions and hence the possibility of testing the Skyrme model against experiment.

hep-th↗