arXiv subjects
Publications and source records attributed to Ruth Durrer.
Structure formation with topological defects is described. The main differences from inflationary models are highlighted. The results are compared with recent observations. It is concluded that all the defect models studied so far are in disagreement with recent observations of CMB anisotropies. Furthermore, present observations do not support 'decoherence', a generic feature of structure formation from topological defects.
We compute the energy spectra for massless Kalb-Ramond axions in four-dimensional anisotropic string cosmological models. We show that, when integrated over directions, the four-dimensional anisotropic model leads to infra-red divergent spectra similar to the one found in the isotropic case.
In this letter we show that in a Gaussian random field the correlation length, the typical size of correlated structures, does not change with biasing. We interpret the amplification of the correlation functions of subsets identified by different thresholds being due to the increasing sparseness of peaks over threshold. This clarifies an long-standing misconception in the literature. We also argue that this effect does not explain the observed increase of the amplitude of the correlation function xi(r) when galaxies of brighter luminosity or galaxy clusters of increasing richness are considered.
In this letter we investigate whether the isotropy problem is naturally solved in inflationary cosmologies inspired by string theory, so called pre-big-bang cosmologies. We find that, in contrast to what happens in the more common 'potential inflation' models, initial anisotropies do not decay during pre-big-bang inflation.
We investigate the global texture model of structure formation in cosmogonies with non-zero cosmological constant for different values of the Hubble parameter. We find that the absence of significant acoustic peaks and little power on large scales are robust predictions of these models. However, from a careful comparison with experiments we conclude that at present we cannot safely reject the model on the grounds of published CMB anisotropy data. If bias is close to one on large scales, galaxy correlation data rules out the models. New, very stringent constraints come from peculiar velocities. Investigating the large-N limit, we argue that our main conclusions apply to all global O(N) models of structure formation.
We consider harmonic maps from Minkowski space into the three sphere. We are especially interested in solutions which are asymptotically constant, i.e. converge to the same value in all directions of spatial infinity. Physical 3-space can then be compactified and can be identified topologically (but not metrically!) with a three sphere. Therefore, at fixed time, the winding of the map is defined. We investigate whether static solutions with non-trivial winding number exist. The answer which we can proof here is only partial: We show that within a certain family of maps no static solutions with non-zero winding number exist. We discuss the existing static solutions in our family of maps. An extension to other maps or a proof that our family of maps is sufficiently general remains an open problem.
We derive a simple closed-form expression, relating $\vs(r)$ -- the mean relative velocity of pairs of galaxies at fixed separation $r$ -- to the two-point correlation function of mass density fluctuations, $ξ(r)$. We compare our analytic model for $\vs(r)$ with N-body simulations, and find excellent agreement in the entire dynamical range probed by the simulations ($0.1 \lsim ξ\lsim 1000$). Our results can be used to estimate the cosmological density parameter, $\Om$, directly from redshift-distance surveys, like Mark III.
We investigate the global texture model of structure formation in cosmogonies with non-zero cosmological constant for different values of the Hubble parameter. We find that the absence of significant acoustic peaks and little power on large scales are robust predictions of these models. However, from a careful comparison with data we conclude that at present we cannot safely reject the model on the grounds of present CMB data. Exclusion by means of galaxy correlation data requires assumptions on biasing and statistics. New, very stringent constraints come from peculiar velocities. Investigating the large-N limit, we argue that our main conclusions apply to all global O(N) models of structure formation.
In this letter we present an idea which reconciles a homogeneous and isotropic Friedmann universe with a fractal distribution of galaxies. We use two observational facts: The flat rotation curves of galaxies and the (still debated) fractal distribution of galaxies with fractal dimension D=2. Our idea can also be interpreted as a redefinition of the notion of bias.
We investigate microwave background anisotropies in the presence of primordial magnetic fields. We show that a homogeneous field with fixed direction can amplify vector perturbations. We calculate the correlations of $δT/T$ explicitly and show that a large scale coherent field induces correlations between $a_{\ell-1,m}$ and $a_{\ell+1,m}$. We discuss constraints on amplitude and spectrum of a primordial magnetic field imposed by observations of CMB anisotropies.
Anisotropies in the cosmic microwave background radiation due to gravity waves are investigated. An initial spectrum of gravity waves may have been induced during an epoch of inflation. We study the propagation of such a spectrum in a Friedmann background of hot and cold dark matter, radiation and (possibly) a cosmological constant. We finally calculate its imprint as anisotropies on the cosmic microwave background. We also take into account that massless particles can source gravity waves by their anisotropic stresses. We consider general mixed dark matter models with and without cosmological constant. For a given, scale invariant input spectrum of gravity we determine the dependence of the resulting spectrum of CMB anisotropies on the different model parameters.
In this work we present a partially new method to analyze fluctuations which are induced by causal scaling seeds. We show that the power spectra due to this kind of seed perturbations are determined by five analytic functions, which we determine numerically for a special example. We put forward the view that, even if recent work disfavors the models with cosmic strings and global O(4) texture, causal scaling seed perturbations merit a more thorough and general analysis, which we initiate in this paper.
We discuss various questions which arise when one considers the central projection of three dimensional fractal sets (galaxy catalogs) onto the celestial globe. The issues are related to how fractal such projections look. First we show that the lacunarity in the projection can be arbitrarily small. Further characteristics of the projected set---in particular scaling---depend sensitively on how the apparent sizes of galaxies are taken into account. Finally, we discuss the influence of opacity of galaxies. Combining these ideas, seemingly contradictory statements about lacunarity and apparent projections can be reconciled.
We study microwave background anisotropies induced by scaling seed perturbations in a universe dominated by cold dark matter. Using a gauge invariant linear perturbation analysis, we solve the perturbation equations on super-horizon scales, for CMB anisotropies triggered by generic gravitational seeds. We find that perturbations induced by seeds --- under very mild restrictions --- are nearly isocurvature. Thus, compensation, which is mainly the consequence of physically sensible initial conditions, is very generic. We then restrict our study to the case of scaling sources, motivated by global scalar fields. We parameterize the energy momentum tensor of the source by ``seed functions'' and calculate the Sachs-Wolfe and acoustic contributions to the CMB anisotropies. We discuss the dependence of the anisotropy spectrum on the parameters of the model considered. Even within the restricted class of models investigated in this work, we find a surprising variety of results for the position and height of the first acoustic peak as well as for the overall amplitude. In particular, for certain choices of parameters, the spectrum resembles very much the well known adiabatic inflationary spectrum, whereas for others, the position of the first acoustic peak is significantly shifted towards smaller angular scales.
An introduction to topological defects in cosmology is given. We discuss their possible relevance for structure formation. Especial emphasis is given on the signature of topological defects in the spectrum of anisotropies in the cosmic microwave background. We present simple analytic estimates for the CMB spectrum on large and intermediate scales and compare them with the corresponding approximations for models where initial perturbations are generated during an inflationary epoch.
We present an analysis of CMB anisotropies induced by global scalar fields in the large N limit. In this limit, the CMB anisotropy spectrum can be determined without cumbersome 3D simulations. We determine the source functions and their unequal time correlation functions and show that they are quite similar to the corresponding functions in the texture model. This leads us to the conclusion that the large N limit provides a 'cheap approximation' to the texture model of structure formation.
The analysis of anisotropies in the cosmic microwave background (CMB) has become an extremely valuable tool for cosmology. We even have hopes that planned CMB anisotropy experiments may revolutionize cosmology. Together with determinations of the CMB spectrum, they represent the first cosmological precision measurements. This is illustrated in the talk by Anthony Lasenby. The value of CMB anisotropies lies to a big part in the simplicity of the theoretical analysis. Fluctuations in the CMB can be determined almost fully within linear cosmological perturbations theory and are not severely influenced by complicated nonlinear physics. In this contribution the different physical processes causing or influencing anisotropies in the CMB are discussed. The geometry perturbations at and after last scattering, the acoustic oscillations in the baryon-photon-plasma prior to recombination, and the diffusion damping during the process of recombination. The perturbations due to the fluctuating gravitational field, the so called Sachs-Wolfe contribution, is described in a very general form using the Weyl tensor of the perturbed geometry.
We review recent work aimed at showing how global topological defects influence the shape of the angular power spectrum of the CMB radiation on small scales. While Sachs-Wolfe fluctuations give the dominant contribution on angular scales larger than about a few degrees, on intermediate scales the main rôle is played by coherent oscillations in the baryon radiation plasma before recombination. In standard cosmological models these oscillations lead to the `Doppler peaks' in the angular power spectrum. Inflation-based cold dark matter models predict the location of the first peak to be at $\ell\sim 220/\sqrt{Ω_0}$, with a height which is a few times the level of anisotropies at large scales. Here we focus on perturbations induced by global textures. We find that the height of the first peak is reduced and is shifted to $\ell\sim 350$.