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Boudewijn F. Roukema

Publications and source records attributed to Boudewijn F. Roukema.

At least 73 records · Page 4Linked to original sources
arXiv2005

Cosmic crystallography using short-lived objects - active galactic nuclei

Cosmic crystallography is based on the principle that peaks in the pair separation histogram (PSH) of objects in a catalogue should be induced by the high number of topologically lensed pairs that are separated by Clifford translations, in excess to ``random'' pairs of objects. Here we present modifications of this method that successively improve the signal-to-noise ratio by removing a large part of the noise and then false signals induced by selection effects. Given the transient nature of the most readily available tracer objects, active galactic nuclei (AGNs), the former is possible because a natural filter for removing many of the noise pairs is available: when counting pairs of objects in order to create PSHs, only those with nearly identical redshifts need to be counted. This redshift filter (a maximum value of $Δz/z = 0.005$) was applied to a compilation of AGN catalogues. Further noise was removed by applying a second filter, a maximum angle $Δθ=0.075$ rad, and a minimum number of pairs $\protect\npairs=3$ to find each ``bunch of pairs'' (BoP) where the {\em vectors} (in Euclidean comoving space) defined by pairs are required to be nearly equal, whereas in the PSH only the {\em lengths} must be nearly equal. These filters reveal significant signals, which, however, are due to selection effects. A third filter, a minimum length $\Lselec=150$ {\hMpc} between the (parallel) vectors in a BoP, is found to effectively remove these selection effect pairs. After application of these successive filters, no significant topological signal was found.

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arXiv2004

A Solution to the Isolatitude, Equi-area, Hierarchical Pixel-Coordinate System

Gorski et al (1999b) have earlier presented the outline of a pixelisation-to-spherical-coordinate transformation scheme which simultaneously satisfies three properties which are especially useful for rapid analyses of maps on a sphere: (i) equal spacing of pixels along lines of constant latitude, (ii) equal pixel `areas' (solid angles) and (iii) hierarchical scaling with increasing numbers of pixels. Their outline is based on the division of the sphere into twelve regions covering equal solid angles, which are hierarchically subdivided in a way compatible with these three criteria. In this paper, a complete derivation of this scheme is presented, including, in particular, (1) the angle theta^* defining the limit between polar and equatorial regions, and (2) the transformations from the unit interval [0,1] \wedge [0,1] to spherical coordinates in a polar region.

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arXiv2004

A Hint of Poincaré Dodecahedral Topology in the WMAP First Year Sky Map

Luminet et al. (2003) suggested that WMAP data are better matched by a Poincaré dodecahedral FLRW model of global geometry, rather than by an infinite flat model. The analysis by Cornish et al. (2003) for angular radii 25-90 degrees failed to support this. Here, a matched circles analysis specifically designed to detect dodecahedral patterns of matched circles is performed over angular radii in the range 1-40 degrees on the one-year WMAP ILC map, using a correlation statistic and an rms difference statistic. Extreme value distributions of these statistics are calculated for left-handed and right-handed 36 degree `screw motions' (Clifford translations) when matching circles and for a zero (unphysical) rotation. The most correlated circles appear for circle radii of 11\pm1 degrees, for the left-handed screw motion, but not for the right-handed one, nor for the zero rotation. The favoured six dodecahedral face centres in galactic coordinates are (l,b)= (252, +65), (51, +51), (144,+38), (207,+10), (271,+3), (332,+25) and their opposites. The six pairs of circles_independently_ each favour a circle angular radius of 11\pm1 degrees. Whether or not these six circle pairs centred on dodecahedral faces match via a 36 degree rotation only due to unexpected statistical properties of the WMAP ILC map, or whether they match due to global geometry, it is clear that the WMAP ILC map has some unusual statistical properties which mimic a potentially interesting cosmological signal. The software for reading the WMAP data and for carrying out this analysis are released under the GNU General Public License.

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arXiv2001

The Milky Way as the Ultimate Extragalactic Source

The GAIA satellite will observe the Galaxy and its closest satellites in great detail. This should allow (i) dating past events of dwarf galaxies merging or interacting with the Galaxy, and much improved orbital parameters of the nine dwarf spheroidals and the Magellanic Clouds and (ii) dating of active galactic nucleus (AGN) phases of the Galaxy several Gigayears in the past, by detecting coeval star formation (e.g. open star clusters) that occurred along kpc scale Galactic jets. Both predictions (i) and (ii) of past history will be highly valuable for searching for or excluding topologically lensed images of the Milky Way at high redshift.

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arXiv2001

On the comoving distance as an arc-length in four dimensions

The inner product provides a conceptually and algorithmically simple method for calculating the comoving distance between two cosmological objects given their redshifts, right ascension and declination, and arbitrary constant curvature. The key to this is that just as a distance between two points `on' the surface of the ordinary 2-sphere ${\cal S}^2$ is simply an arc-length (angle multiplied by radius) in ordinary Euclidean 3-space ${\cal E}^3$, the distance between two points `on' a 3-sphere ${\cal S}^3$ (a 3-hyperboloid ${\cal H}^3$) is simply an `arc-length' in Euclidean 4-space ${\cal E}^4$ (Minkowski 4-space ${\cal M}^4$), i.e. an `hyper-angle' multiplied by the curvature radius of the 3-sphere (3-hyperboloid).

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arXiv2001

How to distinguish a nearly flat Universe from a flat Universe using the orientation independence of a comoving standard ruler

Several recent observations using standard rulers and standard candles now suggest, either individually or in combination, that the Universe is close to flat, i.e. that the curvature radius is about as large as the horizon radius (\sim 10h^{-1}Gpc) or larger. Here, a method of distinguishing an almost flat universe from a precisely flat universe using a single observational data set, without using any microwave background information, is presented. The method (i) assumes that a standard ruler should have no preferred orientation (radial versus tangential) to the observer, and (ii) requires that the (comoving) length of the standard ruler be known independently (e.g. from low redshift estimates). The claimed feature at fixed {\em comoving} length in the power spectrum of density perturbations, detected among quasars, Lyman break galaxies or other high redshift objects, would provide an adequate standard candle to prove that the Universe is curved, if indeed it is curved. For example, a combined intrinsic and measurement uncertainty of 1% in the length of the standard ruler $\llss$ applied at a redshift of $z=3$ would distinguish an hyperbolic $(Ω_m=0.2,Ω_Λ=0.7)$ or a spherical $(Ω_m=0.4,Ω_Λ=0.7)$ universe from a flat one to 1-P > 95% confidence.

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arXiv2001

How to Avoid the Ambiguity in Applying the Copernican Principle for Cosmic Topology: Take the Observational Approach

It is often stated that homogeneity and isotropy of the Universe are assumptions of the almost Friedmann-Lema^itre (FL) model (the hot big bang model), inspired from the Copernican Principle. However, only local homogeneity and isotropy are required by the model: multiply connected almost FL models are locally homogeneous and isotropic, but they can be globally anisotropic and/or globally inhomogeneous. Toy models are used here to show how global anisotropy and/or global inhomogeneity of an almost FL model could be shown directly in observations. This approach may avoid having to make any assumptions regarding global anisotropy and inhomogeneity.

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arXiv2000

Lifting cosmic degeneracy within a single quasar survey

In the almost Friedmann-Lema^itre model of the Universe, the density parameter, Omega_matter, and the cosmological constant, Omega_Lambda, measure curvature. Several linearly degenerate relations between these two parameters have recently been measured. Here, large scale structure correlations at \~100-150 h^-1 Mpc are found in the comoving three-dimensional separations of redshift z \approx 2 quasars. These function as a comoving standard rod of length L_LSS \approx 130+-10 h^-1 Mpc. A local maximum in the correlation function at \approx L_LSS/2 also appears to be significant. By combining separate radial and tangential standard ruler analyses, the lifting of the Omega_matter - Omega_Lambda linear degeneracy within a single data set is demonstrated for the first time.

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arXiv2000

The Topology of the Universe

The Hilbert-Einstein equations are insufficient to describe the geometry of the Universe, as they only constrain a local geometrical property: curvature. A global knowledge of the geometry of space, if possible, would require measurement of the topology of the Universe. Since the subject was discussed in 1900 by Schwarzschild, observational attempts to measure global topology have been rare for most of this century, but have accelerated in the 1990's due to the rapidly increasing amount of observations of non-negligible fractions of the observational sphere. A brief review of basic concepts of cosmic topology and of the rapidly growing gamut of diverse and complementary observational strategies for measuring the topology of the Universe is provided here.

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arXiv2000

Cosmological Topology in Paris 1998

Quel est, ou pourrait être, la topologie globale de la partie spatiale de l'Univers ? L'Univers entier (précisément, l'hypersurface spatiale de celui-ci) est-il observable ? Les mathématiciens, les physiciens et les cosmologistes observationnels ont des approches différentes pour aborder ces questions qui restent ouvertes. What is, or could be, the global topology of spatial sections of the Universe? Is the entire Universe (spatial hypersurface thereof) observable ? Mathematicians, physicists and observational cosmologists have different strategies to approaching these questions which are not yet fully answered.

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arXiv2000

A Counterexample to Claimed COBE Constraints on Compact Toroidal Universe Models

It has been suggested that if the Universe satisfies a flat, multiply connected, perturbed Friedmann-Lema^itre model, then cosmic microwave background data from the COBE satellite implies that the minimum size of the injectivity diameter (shortest closed spatial geodesic) must be larger than about two fifths of the horizon diameter. To show that this claim is misleading, a simple $T^2 \times R$ universe model of injectivity diameter a quarter of this size, i.e. a tenth of the horizon diameter, is shown to be consistent with COBE four year observational maps of the cosmic microwave background. This is done using the identified circles principle.

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arXiv2000

Tangential Large Scale Structure as a Standard Ruler: Curvature Parameters from Quasars

Several observational analyses suggest that matter is spatially structured at $\approx 130h^{-1}Mpc$ at low redshifts. This peak in the power spectrum provides a standard ruler in comoving space which can be used to compare the local geometry at high and low redshifts, thereby constraining the curvature parameters. It is shown here that this power spectrum peak is present in the observed quasar distribution at $z\sim 2$: qualitatively, via wedge diagrams which clearly show a void-like structure, and quantitatively, via one-dimensional Fourier analysis of the quasars' tangential distribution. The sample studied here contains 812 quasars. The method produces strong constraints (68% confidence limits) on the density parameter $Ω_0$ and weaker constraints on the cosmological constant $λ_0$, which can be expressed by the relation $ Ω_0 = (0.24 \pm0.15) + (0.10\pm0.08) λ_0 $. Independently of $λ_0$ (in the range $λ_0 \in [0,1]$), the constraint is $0.1 < Ω_0 < 0.45$. Combination of the present results with SN Type Ia results yields $Ω_0 = (0.30\pm0.11) + (0.57\pm0.11) (λ_0-0.7),$ $0.55 < λ_0 < 0.95,$ (68% confidence limits). This strongly supports the possibility that the observable universe satisfies a nearly flat, perturbed Friedmann-Lema\^ıtre-Robertson-Walker model, independently of any cosmic microwave background observations.

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arXiv1999

Evolution of the correlation function as traced by the HDF galaxies

An initially highly biased value of the spatial correlation function, which decreases with time up to a transition redshift z_t ~ 1-2, was predicted theoretically at least as early as 1993, and shown to be consistent with the HDF-N angular correlation function estimates in 1997. Observational analyses are presented here which show (i) an HDF-N estimate of the correlation function amplitude of galaxies selected at z ~ 2 (by the UV drop-{\em in} technique), which supports the estimate z_t ~ 2 and (ii) an HDF-N estimate of the correlation function amplitude of galaxies selected at z ~ 3.7 by using photometric redshifts, which suggests that the correlation function amplitude evolves as (1+z)^{2\pm3.5} during epochs earlier than z_t.

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arXiv1999

COBE and Global Topology: An Example of the Application of the Identified Circles Principle

The significance to which the cosmic microwave background observations by the satellite COBE can be used to refute a specific observationally based hypothesis for the global topology (3-manifold) of the Universe is investigated, by a new method of applying the principle of matched circle pairs. Moreover, it is shown that this can be done without assuming Gaussian distributions for the density perturbation spectrum. The Universe is assumed to correspond to a flat Friedmann-Lema\^ıtre model with a zero value of the cosmological constant. The 3-manifold is hypothesised to be a 2-torus in two directions, with a third axis larger than the horizon diameter. The positions and lengths of the axes are determined by the relative positions of the galaxy clusters Coma, RX~J1347.5-1145 and CL 09104+4109, assumed to be multiple topological images of a single, physical cluster. If the following two assumptions are valid: (i) the error estimates in the COBE DMR data are accurate estimates of the total random plus systematic error; and (ii) the temperature fluctuations are dominated by the na\"ıve Sachs-Wolfe effect; then the distribution of the temperature differences between multiply imaged pixels is significantly wider than the uncertainty in the differences, and the candidate is rejected at the 94% level. This result is valid for either the `subtracted' or `combined' Analysed Science Data Sets, for either $10°$ or $20°$ smoothing, and is strengthened if suspected contaminated regions from the galactic centre and the Ophiuchus and Orion complexes are removed.

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arXiv1999

Topology of the Universe: Theory and Observations

``One could imagine that as a result of enormously extended astronomical experience, the entire universe consists of countless identical copies of our Milky Way, that the infinite space can be partitioned into cubes each containing an exactly identical copy of our Milky Way. Would we really cling on to the assumption of infinitely many identical repetitions of the same world? >... We would be much happier with the view that these repetitions are illusory, that in reality space has peculiar connection properties so that if we leave any one cube through a side, then we immediately reenter it through the opposite side.'' (Schwarzschild 1900, translation 1998) Developments in the theoretical and observational sides of cosmic topology were slow for most of the century, but are now progressing rapidly, at the scale of most interest which is 1-10 h^-1 Gpc rather than 10kpc. The historical, mathematical and observational sides of this subject are briefly reviewed in this course.

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arXiv1999

Constraining Curvature Parameters via Topology

If the assumption that physical space has a trivial topology is dropped, then the Universe may be described by a multiply connected Friedmann-Lema\^ıtre model on a sub-horizon scale. Specific candidates for the multiply connected space manifold have already been suggested. How precisely would a significant detection of multiple topological images of a single object, or a region on the cosmic microwave background, (due to photons arriving at the observer by multiple paths which have crossed the Universe in different directions), constrain the values of the curvature parameters $Ω_0$ and $λ_0$? The way that the constraints on $Ω_0$ and $λ_0$ depend on the redshifts of multiple topological images and on their radial and tangential separations is presented and calculated. The tangential separations give the tighter constraints: multiple topological images of known types of astrophysical objects at redshifts $z \ltapprox 3$ would imply values of $Ω_0$ and $λ_0$ preciser than $\sim 1%$ and $\sim 10%$ respectively. Cosmic microwave background `spots' identified with lower redshift objects by the Planck or MAP satellites would provide similar precision. This method is purely geometrical: no dynamical assumptions (such as the virial theorem) are required and the constraints are independent of the Hubble constant, $H_0.$

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arXiv1999

Topology of the Universe: background and recent observational approaches

Is the Universe (a spatial section thereof) finite or infinite? Knowing the global geometry of a Friedmann-Lema\^ıtre (FL) universe requires knowing both its curvature and its topology. A flat or hyperbolic (``open'') FL universe is {\em not} necessarily infinite in volume. Multiply connected flat and hyperbolic models are, in general, as consistent with present observations on scales of 1-20{\hGpc} as are the corresponding simply connected flat and hyperbolic models. The methods of detecting multiply connected models (MCM's) are presently in their pioneering phase of development and the optimal observationally realistic strategy is probably yet to be calculated. Constraints against MCM's on ~1-4 h^{-1} Gpc scales have been claimed, but relate more to inconsistent assumptions on perturbation statistics rather than just to topology. Candidate 3-manifolds based on hypothesised multiply imaged objects are being offered for observational refutation. The theoretical and observational sides of this rapidly developing subject have yet to make any serious contact, but the prospects of a significant detection in the coming decade may well propel the two together.

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