1,224 research outputs found
Where are the Hedgehogs in Nematics?
In experiments which take a liquid crystal rapidly from the isotropic to the
nematic phase, a dense tangle of defects is formed. In nematics, there are in
principle both line and point defects (``hedgehogs''), but no point defects are
observed until the defect network has coarsened appreciably. In this letter the
expected density of point defects is shown to be extremely low, approximately
per initially correlated domain, as result of the topology
(specifically, the homology) of the order parameter space.Comment: 6 pages, latex, 1 figure (self-unpacking PostScript)
Correlations in Cosmic String Networks
We investigate scaling and correlations of the energy and momentum in an
evolving network of cosmic strings in Minkowski space. These quantities are of
great interest, as they must be understood before accurate predictions for the
power spectra of the perturbations in the matter and radiation in the early
Universe can be made. We argue that Minkowski space provides a reasonable
approximation to a Friedmann background for string dynamics and we use our
results to construct a simple model of the network, in which it is considered
to consist of randomly placed segments moving with random velocities. This
model works well in accounting for features of the two-time correlation
functions, and even better for the power spectra.Comment: 20pp Plain LaTeX, 11 EPS figures, uses epsf.st
Large Radius Hagedorn Regime in String Gas Cosmology
We calculate the equation of state of a gas of strings at high density in a
large toroidal universe, and use it to determine the cosmological evolution of
background metric and dilaton fields in the entire large radius Hagedorn
regime, (ln S)^{1/d} << R << S^{1/d} (with S the total entropy). The pressure
in this regime is not vanishing but of O(1), while the equation of state is
proportional to volume, which makes our solutions significantly different from
previously published approximate solutions. For example, we are able to
calculate the duration of the high-density "Hagedorn" phase, which increases
exponentially with increasing entropy, S. We go on to discuss the difficulties
of the scenario, quantifying the problems of establishing thermal equilibrium
and producing a large but not too weakly-coupled universe.Comment: 12 pages, 4 figures, more details presented in string thermodynamics
section, to be published in Physical Review
Defect formation and local gauge invariance
We propose a new mechanism for formation of topological defects in a U(1)
model with a local gauge symmetry. This mechanism leads to definite
predictions, which are qualitatively different from those of the Kibble-Zurek
mechanism of global theories. We confirm these predictions in numerical
simulations, and they can also be tested in superconductor experiments. We
believe that the mechanism generalizes to more complicated theories.Comment: REVTeX, 4 pages, 2 figures. The explicit form of the Hamiltonian and
the equations of motion added. To appear in PRL (http://prl.aps.org/
Renormalisation group improvement of scalar field inflation
We study quantum corrections to Friedmann-Robertson-Walker cosmology with a
scalar field under the assumption that the dynamics are subject to
renormalisation group improvement. We use the Bianchi identity to relate the
renormalisation group scale to the scale factor and obtain the improved
cosmological evolution equations. We study the solutions of these equations in
the renormalisation group fixed point regime, obtaining the time-dependence of
the scalar field strength and the Hubble parameter in specific models with
monomial and trinomial quartic scalar field potentials. We find that power-law
inflation can be achieved in the renormalisation group fixed point regime with
the trinomial potential, but not with the monomial one. We study the transition
to the quasi-classical regime, where the quantum corrections to the couplings
become small, and find classical dynamics as an attractor solution for late
times. We show that the solution found in the renormalisation group fixed point
regime is also a cosmological fixed point in the autonomous phase space. We
derive the power spectrum of cosmological perturbations and find that the
scalar power spectrum is exactly scale-invariant and bounded up to arbitrarily
small times, while the tensor perturbations are tilted as appropriate for the
background power-law inflation. We specify conditions for the renormalisation
group fixed point values of the couplings under which the amplitudes of the
cosmological perturbations remain small.Comment: 17 pages; 2 figure
Charged Black Cosmic String
Global U(1) strings with cylindrical symmetry are studied in anti-de Sitter
spacetime. According as the magnitude of negative cosmological constant, they
form regular global cosmic strings, extremal black cosmic strings and charged
black cosmic strings, but no curvature singularity is involved. The
relationship between the topological charge of a neutral global string and the
black hole charge is clarified by duality transformation. Physical relevance as
straight string is briefly discussed.Comment: ll pages, LaTe
Cosmic string parameter constraints and model analysis using small scale Cosmic Microwave Background data
We present a significant update of the constraints on the Abelian Higgs
cosmic string tension by cosmic microwave background (CMB) data, enabled both
by the use of new high-resolution CMB data from suborbital experiments as well
as the latest results of the WMAP satellite, and by improved predictions for
the impact of Abelian Higgs cosmic strings on the CMB power spectra. The new
cosmic string spectra (presented in a previous work) were improved especially
for small angular scales, through the use of larger Abelian Higgs string
simulations and careful extrapolation. If Abelian Higgs strings are present
then we find improved bounds on their contribution to the CMB anisotropies,
f10< 0.095, and on their tension, G\mu< 0.57 x 10^-6, both at 95% confidence
level using WMAP7 data; and f10 < 0.048 and G\mu < 0.42 x 10^-6 using all the
CMB data. We also find that using all the CMB data, a scale invariant initial
perturbation spectrum, ns=1, is now disfavoured at 2.4\sigma\ even if strings
are present. A Bayesian model selection analysis no longer indicates a
preference for strings.Comment: 8 pages, 3 figures; Minor corrections, matches published versio
Covariant Closed String Coherent States
We give the first construction of covariant coherent closed string states,
which may be identified with fundamental cosmic strings. We outline the
requirements for a string state to describe a cosmic string, and using DDF
operators provide an explicit and simple map that relates three different
descriptions: classical strings, lightcone gauge quantum states and covariant
vertex operators. The naive construction leads to covariant vertex operators
whose existence requires a lightlike compactification of spacetime. When the
lightlike compactified states in the underlying Hilbert space are projected out
the resulting coherent states have a classical interpretation and are in
one-to-one correspondence with arbitrary classical closed string loops.Comment: 4 page
Universality and Critical Phenomena in String Defect Statistics
The idea of biased symmetries to avoid or alleviate cosmological problems
caused by the appearance of some topological defects is familiar in the context
of domain walls, where the defect statistics lend themselves naturally to a
percolation theory description, and for cosmic strings, where the proportion of
infinite strings can be varied or disappear entirely depending on the bias in
the symmetry. In this paper we measure the initial configurational statistics
of a network of string defects after a symmetry-breaking phase transition with
initial bias in the symmetry of the ground state. Using an improved algorithm,
which is useful for a more general class of self-interacting walks on an
infinite lattice, we extend the work in \cite{MHKS} to better statistics and a
different ground state manifold, namely , and explore various different
discretisations. Within the statistical errors, the critical exponents of the
Hagedorn transition are found to be quite possibly universal and identical to
the critical exponents of three-dimensional bond or site percolation. This
improves our understanding of the percolation theory description of defect
statistics after a biased phase transition, as proposed in \cite{MHKS}. We also
find strong evidence that the existence of infinite strings in the Vachaspati
Vilenkin algorithm is generic to all (string-bearing) vacuum manifolds, all
discretisations thereof, and all regular three-dimensional lattices.Comment: 62 pages, plain LaTeX, macro mathsymb.sty included, figures included.
also available on
http://starsky.pcss.maps.susx.ac.uk/groups/pt/preprints/96/96011.ps.g
- …