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.Comment: LaTeX, IMPERIAL/TP/93-94/2

On Random Bubble Lattices

We study random bubble lattices which can be produced by processes such as first order phase transitions, and derive characteristics that are important for understanding the percolation of distinct varieties of bubbles. The results are relevant to the formation of topological defects as they show that infinite domain walls and strings will be produced during appropriate first order transitions, and that the most suitable regular lattice to study defect formation in three dimensions is a face centered cubic lattice. Another application of our work is to the distribution of voids in the large-scale structure of the universe. We argue that the present universe is more akin to a system undergoing a first-order phase transition than to one that is crystallizing, as is implicit in the Voronoi foam description. Based on the picture of a bubbly universe, we predict a mean coordination number for the voids of 13.4. The mean coordination number may also be used as a tool to distinguish between different scenarios for structure formation.Comment: several modifications including new abstract, comparison with froth models, asymptotics of coordination number distribution, further discussion of biased defects, and relevance to large-scale structur

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.Comment: 9 pages ReVTeX, 1 Postscript figure, minor changes for publicatio

Estimate of the Cosmological Bispectrum from the MAXIMA-1 Cosmic Microwave Background Map

We use the measurement of the cosmic microwave background taken during the MAXIMA-1 flight to estimate the bispectrum of cosmological perturbations. We propose an estimator for the bispectrum that is appropriate in the flat sky approximation, apply it to the MAXIMA-1 data and evaluate errors using bootstrap methods. We compare the estimated value with what would be expected if the sky signal were Gaussian and find that it is indeed consistent, with a $\chi^2$ per degree of freedom of approximately unity. This measurement places constraints on models of inflation.Comment: 5 pages, 2 figures. New version to match paper accepted for publication in Phys. Rev. Lett. Non-diagonal terms included leading to new limits on f_N

Determining Foreground Contamination in CMB Observations: Diffuse Galactic Emission in the MAXIMA-I Field

Observations of the CMB can be contaminated by diffuse foreground emission from sources such as Galactic dust and synchrotron radiation. In these cases, the morphology of the contaminating source is known from observations at different frequencies, but not its amplitude at the frequency of interest for the CMB. We develop a technique for accounting for the effects of such emission in this case, and for simultaneously estimating the foreground amplitude in the CMB observations. We apply the technique to CMB data from the MAXIMA-1 experiment, using maps of Galactic dust emission from combinations of IRAS and DIRBE observations, as well as compilations of Galactic synchrotron emission observations. The spectrum of the dust emission over the 150--450 GHz observed by MAXIMA is consistent with preferred models but the effect on CMB power spectrum observations is negligible.Comment: 19 pages, 8 figures, accepted for publication in the Astrophysical Journal. Monor changes to match the published versio

Fast, exact CMB power spectrum estimation for a certain class of observational strategies

We describe a class of observational strategies for probing the anisotropies in the cosmic microwave background (CMB) where the instrument scans on rings which can be combined into an n-torus, the {\em ring torus}. This class has the remarkable property that it allows exact maximum likelihood power spectrum estimation in of order $N^2$ operations (if the size of the data set is $N$) under circumstances which would previously have made this analysis intractable: correlated receiver noise, arbitrary asymmetric beam shapes and far side lobes, non-uniform distribution of integration time on the sky and partial sky coverage. This ease of computation gives us an important theoretical tool for understanding the impact of instrumental effects on CMB observables and hence for the design and analysis of the CMB observations of the future. There are members of this class which closely approximate the MAP and Planck satellite missions. We present a numerical example where we apply our ring torus methods to a simulated data set from a CMB mission covering a 20 degree patch on the sky to compute the maximum likelihood estimate of the power spectrum $C_\ell$ with unprecedented efficiency.Comment: RevTeX, 14 pages, 5 figures. A full resolution version of Figure 1 and additional materials are at http://feynman.princeton.edu/~bwandelt/RT

Making Maps Of The Cosmic Microwave Background: The MAXIMA Example

This work describes Cosmic Microwave Background (CMB) data analysis algorithms and their implementations, developed to produce a pixelized map of the sky and a corresponding pixel-pixel noise correlation matrix from time ordered data for a CMB mapping experiment. We discuss in turn algorithms for estimating noise properties from the time ordered data, techniques for manipulating the time ordered data, and a number of variants of the maximum likelihood map-making procedure. We pay particular attention to issues pertinent to real CMB data, and present ways of incorporating them within the framework of maximum likelihood map-making. Making a map of the sky is shown to be not only an intermediate step rendering an image of the sky, but also an important diagnostic stage, when tests for and/or removal of systematic effects can efficiently be performed. The case under study is the MAXIMA data set. However, the methods discussed are expected to be applicable to the analysis of other current and forthcoming CMB experiments.Comment: Replaced to match the published version, only minor change

Collapse of topological texture

We study analytically the process of a topological texture collapse in the approximation of a scaling ansatz in the nonlinear sigma-model. In this approximation we show that in flat space-time topological texture eventually collapses while in the case of spatially flat expanding universe its fate depends on the rate of expansion. If the universe is inflationary, then there is a possibility that texture will expand eternally; in the case of exponential inflation the texture may also shrink or expand eternally to a finite limiting size, although this behavior is degenerate. In the case of power law noninflationary expansion topological texture eventually collapses. In a cold matter dominated universe we find that texture which is formed comoving with the universe expansion starts collapsing when its spatial size becomes comparable to the Hubble size, which result is in agreement with the previous considerations. In the nonlinear sigma-model approximation we consider also the final stage of the collapsing ellipsoidal topological texture. We show that during collapse of such a texture at least two of its principal dimensions shrink to zero in a similar way, so that their ratio remains finite. The third dimension may remain finite (collapse of cigar type), or it may also shrink to zero similar to the other two dimensions (collapse of scaling type), or shrink to zero similar to the product of the remaining two dimensions (collapse of pancake type).Comment: 23 pages, LaTeX, to be published in Phys. Rev.

Measurement of a Peak in the Cosmic Microwave Background Power Spectrum from the North American test flight of BOOMERANG

We describe a measurement of the angular power spectrum of anisotropies in the Cosmic Microwave Background (CMB) from 0.3 degrees to ~10 degrees from the North American test flight of the BOOMERANG experiment. BOOMERANG is a balloon-borne telescope with a bolometric receiver designed to map CMB anisotropies on a Long Duration Balloon flight. During a 6-hour test flight of a prototype system in 1997, we mapped > 200 square degrees at high galactic latitudes in two bands centered at 90 and 150 GHz with a resolution of 26 and 16.6 arcmin FWHM respectively. Analysis of the maps gives a power spectrum with a peak at angular scales of ~1 degree with an amplitude ~70 uK.Comment: 5 pages, 1 figure LaTeX, emulateapj.st

The evolution of a network of cosmic string loops

We set up and analyse a model for the non-equilibrium evolution of a network of cosmic strings initially containing only loops and no infinite strings. Due to this particular initial condition, our analytical approach differs significantly from existing ones. We describe the average properties of the network in terms of the distribution function n(l,t) dl, the average number of loops per unit volume with physical length between l and l + dl at time t. The dynamical processes which change the length of loops are then estimated and an equation, which we call the `rate equation', is derived for (dn/dt). In a non-expanding universe, the loops should reach the equilibrium distribution predicted by string statistical mechanics. Analysis of the rate equation gives results consistent with this. We then study the rate equation in an expanding universe and suggest that three different final states are possible for the evolving loop network, each of which may well be realised for some initial conditions. If the initial energy density in loops in the radiation era is low, then the loops rapidly disappear. For large initial energy densities, we expect that either infinite strings are formed or that the loops tend towards a scaling solution in the radiation era and then rapidly disappear in the matter era. Such a scenario may be relevant given recent work highlighting the problems with structure formation from the standard cosmic string scenario.Comment: LaTeX, 27 pages, 10 figures included as .eps file