arXiv subjects

Julian Borrill

Publications and source records attributed to Julian Borrill.

52 records · Page 3Linked to original sources

arXiv2004

The angular power spectrum of NVSS radio galaxies

We measure the angular power spectrum of radio galaxies in the NRAO VLA Sky Survey (NVSS) using two independent methods: direct spherical harmonic analysis and maximum likelihood estimation. The results are consistent and can be understood using models for the spatial matter power spectrum and for the redshift distribution of radio galaxies at mJy flux-density levels. A good fit to the angular power spectrum can only be achieved if radio galaxies possess high bias with respect to mass fluctuations; by marginalizing over the other parameters of the model we derive a 68% confidence interval 1.53 < b_0 sigma_8 < 1.87, where b_0 is the linear bias factor for radio galaxies and sigma_8 describes the normalization of the matter power spectrum. Our models indicate that the majority of the signal in the NVSS angular power spectrum is generated at low redshifts. Individual redshifts for the NVSS sources are thus required to alleviate projection effects and probe directly the matter power spectrum on large scales.

astro-ph↗

arXiv2003

Recent Results from the MAXIMA Experiment

MAXIMA is a balloon-borne platform for measuring the anisotropy of the Cosmic Microwave Background (CMB). It has measured the CMB power spectrum with a ten-arcminute FWHM beam, corresponding to a detection of the power spectrum out to spherical harmonic multipole l~1000. The spectrum is consistent with a flat Universe with a nearly scale-invariant initial spectrum of adiabatic density fluctuations. Moreover, the MAXIMA data are free from any notable non-Gaussian contamination and from foreground dust emission. In the same region, the WMAP experiment observes the same structure as that observed by MAXIMA, as evinced by analysis of both maps and power spectra. The next step in the evolution of the MAXIMA program is MAXIPOL, which will observe the polarization of the CMB with comparable resolution and high sensitivity over a small patch of the sky.

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arXiv2002

The evolution and persistence of dumbbells

We use large-scale numerical simulations to study the formation and evolution of non-topological defects in a generalized electroweak phase transition described by the Glashow-Salam-Weinberg model without fermions. Such defects include dumbbells, comprising a pair of monopoles joined by a segment of electroweak string. These exhibit complex dynamics, with some shrinking under the string tension and others growing due to the monopole-antimonopole attractions between near neighbours. We estimate the range of parameters where the network of dumbbells persists, and show that this region is narrower than the region within which infinite straight electroweak strings are perturbatively stable.

hep-ph↗

arXiv2001

The formation rate of semilocal strings

We carry out three-dimensional numerical simulations to investigate the formation rate of semilocal strings. We find that the back-reaction of the gauge fields on the scalar field evolution is substantial, and leads to a significant formation rate in the parameter regime where the semilocal strings are classically stable. The formation rate can be as large as a third of that for cosmic strings, depending on the model parameters.

hep-ph↗

arXiv1999

MADCAP - The Microwave Anisotropy Dataset Computational Analysis Package

Realizing the extraordinary scientific potential of the CMB requires precise measurements of its tiny anisotropies over a significant fraction of the sky at very high resolution. The analysis of the resulting datasets is a serious computational challenge. Existing algorithms require terabytes of memory and hundreds of years of CPU time. We must therefore both maximize our resources by moving to supercomputers and minimize our requirements by algorithmic development. Here we will outline the nature of the challenge, present our current optimal algorithm, and discuss its implementation as the MADCAP software package and application to data from the North American test flight of the joint Italian-U.S. BOOMERanG experiment on the Cray T3E at NERSC and CINECA. A documented beta-release of MADCAP is publicly available at http://cfpa.berkeley.edu/~borrill/cmb/madcap.html

astro-ph↗

arXiv1999

The Challenge Of Data Analysis For Future CMB Observations

Ongoing observations of the Cosmic Microwave Background, such as the MAXIMA and BOOMERanG projects, are providing datasets of unprecedented quality and ever-increasing size. Exact analysis of the data they produce is a serious computational challenge, currently scaling as the number of sky pixels squared in memory and cubed in time. Here we discuss the origins of these scaling relations and their implications for our efforts to extract precise cosmological parameters from observations of the CMB.

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arXiv1998

On the formation of non-topological string networks

We review recent simulations of the formation of a particular class of non-topological defects known as semilocal strings during a phase transition. Semilocal strings have properties that are intermediate between topological cosmic strings and stable electroweak strings, and therefore the observation that they could form in substantial quantities during a cosmological phase transition has implications for structure formation, baryogenesis, etc. At the same time, and from a purely theoretical point of view, they provide a very good testing ground for investigating the role of gauge fields in defect formation.

hep-ph↗

arXiv1998

A Fast Method For Bounding The CMB Power Spectrum Likelihood Function

As the Cosmic Microwave Background (CMB) radiation is observed to higher and higher angular resolution the size of the resulting datasets becomes a serious constraint on their analysis. In particular current algorithms to determine the location of, and curvature at, the peak of the power spectrum likelihood function from a general $N_{p}$-pixel CMB sky map scale as $O(N_{p}^{3})$. Moreover the current best algorithm --- the quadratic estimator --- is a Newton-Raphson iterative scheme and so requires a `sufficiently good' starting point to guarantee convergence to the true maximum. Here we present an algorithm to calculate bounds on the likelihood function at any point in parameter space using Gaussian quadrature and show that, judiciously applied, it scales as only $O(N_{p}^{7/3})$. Although it provides no direct curvature information we show how this approach is well-suited both to estimating cosmological parameters directly and to providing a coarse map of the power spectrum likelihood function from which to select the starting point for more refined techniques.

astro-ph↗

arXiv1998

Semilocal string formation in two dimensions

We present a toy model for the investigation of the formation of semilocal strings, where a planar symmetry is employed to reduce the system to two dimensions. We approximate the symmetry breaking using an extension of the Vachaspati-Vilenkin algorithm, where we throw down random phases for the scalar fields and then find the gauge field configuration which minimizes gradient energy in this fixed scalar background. We show this procedure reproduces the standard estimate for the formation rate of cosmic strings. For semilocal strings the configurations generated by this method are ambiguous, and we numerically evolve the configurations forward in time to identify which regions form strings. We find a significant rate of formation, depending on the ratio of couplings $β$. For low $β$ the formation rate is about one quarter that of cosmic strings; this falls as $β$ is increased and above $β= 1$, where the string solution is dynamically unstable, no semilocal strings form. We show the results are robust by examining different initial conditions where, as expected in a thermal environment, the initial scalar field need not be on the vacuum. We discuss implications for the three-dimensional case.

hep-ph↗

arXiv1997

Power Spectrum Estimators For Large CMB Datasets

Forthcoming high-resolution observations of the Cosmic Microwave Background (CMB) radiation will generate datasets many orders of magnitude larger than have been obtained to date. The size and complexity of such datasets presents a very serious challenge to analysing them with existing or anticipated computers. Here we present an investigation of the currently favored algorithm for obtaining the power spectrum from a sky-temperature map --- the quadratic estimator. We show that, whilst improving on direct evaluation of the likelihood function, current implementations still inherently scale as the equivalent of the cube of the number of pixels or worse, and demonstrate the critical importance of choosing the right implementation for a particular dataset.

astro-ph↗

arXiv1996

Matching numerical simulations to continuum field theories: A lattice renormalization study

The study of nonlinear phenomena in systems with many degrees of freedom often relies on complex numerical simulations. In trying to model realistic situations, these systems may be coupled to an external environment which drives their dynamics. For nonlinear field theories coupled to thermal (or quantum) baths, discrete lattice formulations must be dealt with extreme care if the results of the simulations are to be interpreted in the continuum limit. Using techniques from renormalization theory, a self-consistent method is presented to match lattice results to continuum models. As an application, symmetry restoration in $ϕ^4$ models is investigated.

hep-lat↗

arXiv1996

On The Absence Of Open Strings In A Lattice-Free Simulation Of Cosmic String Formation

Lattice-based string formation algorithms can, at least in principle, be reduced to the study of the statistics of the corresponding aperiodic random walk. Since in three or more dimensions such walks are transient this approach necessarily generates a population of open strings. To investigate whether open strings are an artefact of the lattice we develop an alternative lattice-free simulation of string formation. Replacing the lattice with a graph generated by a minimal dynamical model of a first order phase transition we obtain results consistent with the hypothesis that the energy density in string is due to a scale-invariant Brownian distribution of closed loops alone.

hep-ph↗

arXiv1995

Defect Production in Slow First Order Phase Transitions

We study the formation of vortices in a U(1) gauge theory following a first-order transition proceeding by bubble nucleation, in particular the effect of a low velocity of expansion of the bubble walls. To do this, we use a two-dimensional model in which bubbles are nucleated at random points in a plane and at random times and then expand at some velocity $v_{\rm b}<c$. Within each bubble, the phase angle is assigned one of three discrete values. When bubbles collide, magnetic `fluxons' appear: if the phases are different, a fluxon--anti-fluxon pair is formed. These fluxons are eventually trapped in three-bubble collisions when they may annihilate or form quantized vortices. We study in particular the effect of changing the bubble expansion speed on the vortex density and the extent of vortex--anti-vortex correlation.

hep-ph↗

arXiv1994

Thermal Phase Mixing During First Order Phase Transitions

The dynamics of first order phase transitions are studied in the context of (3+1)-dimensional scalar field theories. Particular attention is paid to the question of quantifying the strength of the transition, and how `weak' and `strong' transitions have different dynamics. We propose a model with two available low temperature phases separated by an energy barrier so that one of them becomes metastable below the critical temperature $T_c$. The system is initially prepared in this phase and is coupled to a thermal bath. Investigating the system at its critical temperature, we find that `strong' transitions are characterized by the system remaining localized within its initial phase, while `weak' transitions are characterized by considerable phase mixing. Always at $T_c$, we argue that the two regimes are themselves separated by a (second order) phase transition, with an order parameter given by the fractional population difference between the two phases and a control parameter given by the strength of the scalar field's quartic self-coupling constant. We obtain a Ginzburg-like criterion to distinguish between `weak' and `strong' transitions, in agreement with previous results in (2+1)-dimensions.

hep-ph↗

arXiv1994

Numerical Methods in Cosmological Global Texture Simulations

Numerical simulations of the evolution of a global topological defect field have two characteristic length scales --- one macrophysical, of order the field correlation length, and the other microphysical, of order the field width. The situation currently of most interest to particle cosmologists involves the behaviour of a GUT-scale defect field at the epoch of decoupling, where the ratio of these scales is typically of order $10^{50}$. Such a ratio is unrealisable in numerical work, and we consider the approximations which may be employed to deal with this. Focusing on the case of global texture we outline the implementation of the associated algorithms, and in particular note the subtleties involved in handling texture unwinding events. Comparing the results in each approach then establishes that, subject to certain constraints on the minimum grid resolution, the methods described are both robust and consistent with one another.

astro-ph↗

arXiv1994

Texture-Induced Microwave Background Anisotropies

We use numerical simulations to calculate the cosmic microwave background anisotropy induced by the evolution of a global texture field, with special emphasis on individual textures. Both spherically symmetric and general configurations are analysed, and in the latter case we consider field configurations which exhibit unwinding events and also ones which do not. We compare the results given by evolving the field numerically under both the expanded core (XCORE) and non-linear sigma model (NLSM) approximations with the analytic predictions of the NLSM exact solution for a spherically symmetric self-similar (SSSS) unwinding. We find that the random unwinding configuration spots' typical peak height is 60--75\% and angular size typically only 10\% of those of the SSSS unwinding, and that random configurations without an unwinding event nonetheless may generate indistinguishable hot and cold spots. The influence of these results on analytic estimates of texture induced microwave anisotropies is examined, and comparison made with other numerical work.

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