Searcharxiv⌕ Search

arXiv subjects

F. Steiner

Publications and source records attributed to F. Steiner.

16 recordsLinked to original sources
arXiv2009

Hot pixel contamination in the CMB correlation function?

Recently, it was suggested that the map-making procedure, which is applied to the time-ordered CMB data by the WMAP team, might be flawed by hot pixels. This could lead to a bias in the pixels having an angular distance of about 141 degrees from hot pixels due to the differential measuring process of the satellite WMAP. Here, the bias is confirmed, and the temperature two-point correlation function C(theta) is reevaluated by excluding the affected pixels. It is shown that the most significant effect occurs in C(theta) at the largest angles near theta = 180 degrees. Furthermore, the corrected correlation function C(theta) is applied to the cubic topology of the Universe, and it is found that such a multi-connected universe matches the temperature correlation better than the LCDM concordance model, provided the cubic length scale is close to L=4 measured in units of the Hubble length.

astro-ph.CO↗
arXiv2008

A 24-h forecast of ozone peaks and exceedance levels using neural classifiers and weather predictions

A neural network combined to a neural classifier is used in a real time forecasting of hourly maximum ozone in the centre of France, in an urban atmosphere. This neural model is based on the MultiLayer Perceptron (MLP) structure. The inputs of the statistical network are model output statistics of the weather predictions from the French National Weather Service. With this neural classifier, the Success Index of forecasting is 78% whereas it is from 65% to 72% with the classical MLPs. During the validation phase, in the Summer of 2003, six ozone peaks above the threshold were detected. They actually were seven.

stat.AP↗
arXiv2006

CMB Alignment in Multi-Connected Universes

The low multipoles of the cosmic microwave background (CMB) anisotropy possess some strange properties like the alignment of the quadrupole and the octopole, and the extreme planarity or the extreme sphericity of some multipoles, respectively. In this paper the CMB anisotropy of several multi-connected space forms is investigated with respect to the maximal angular momentum dispersion and the Maxwellian multipole vectors in order to settle the question whether such spaces can explain the low multipole anomalies in the CMB.

astro-ph↗
arXiv2005

The circles-in-the-sky signature for three spherical universes

The mysteriously low CMB power on the largest scales might point to a Universe which consists of a multi-connected space. In addition to a suppression of large-scale power, a multi-connected space can be revealed by its circles-in-the-sky signature. In this paper, a detailed search for this signature is carried out for those three homogeneous multi-connected spherical space forms that lead to the smallest large-scale power. A simultaneous search for all occurring paired circles is made using filtered CMB sky maps which enhance the ordinary Sachs-Wolfe contribution. A marginal hint is found for the right-handed Poincare dodecahedron at Omega_tot = 1.015 and for the right-handed binary tetrahedral space at Omega_tot = 1.068. However, due to the complicated noise and foreground structure of the available microwave sky maps, we cannot draw firm conclusions from our findings.

astro-ph↗
arXiv2005

CMB Anisotropy of Spherical Spaces

The first-year WMAP data taken at their face value hint that the Universe might be slightly positively curved and therefore necessarily finite, since all spherical (Clifford-Klein) space forms M^3 = S^3/Gamma, given by the quotient of S^3 by a group Gamma of covering transformations, possess this property. We examine the anisotropy of the cosmic microwave background (CMB) for all typical groups Gamma corresponding to homogeneous universes. The CMB angular power spectrum and the temperature correlation function are computed for the homogeneous spaces as a function of the total energy density parameter Omega_tot in the large range [1.01, 1.20] and are compared with the WMAP data. We find that out of the infinitely many homogeneous spaces only the three corresponding to the binary dihedral group T*, the binary octahedral group O*, and the binary icosahedral group I* are in agreement with the WMAP observations. Furthermore, if Omega_tot is restricted to the interval [1.00, 1.04], the space described by T* is excluded since it requires a value of Omega_tot which is probably too large being in the range [1.06, 1.07]. We thus conclude that there remain only the two homogeneous spherical spaces S^3/O* and S^3/I* with Omega_tot of about 1.038 and 1.018, respectively, as possible topologies for our Universe.

astro-ph↗
arXiv2005

CMB Anisotropy of the Poincare Dodecahedron

We analyse the anisotropy of the cosmic microwave background (CMB) for the Poincare dodecahedron which is an example for a multi-connected spherical universe. We compare the temperature correlation function and the angular power spectrum for the Poincare dodecahedral universe with the first-year WMAP data and find that this multi-connected universe can explain the surprisingly low CMB anisotropy on large scales found by WMAP provided that the total energy density parameter Omega_tot is in the range 1.016...1.020. The ensemble average over the primordial perturbations is assumed to be the scale-invariant Harrison-Zel'dovich spectrum. The circles-in-the-sky signature is studied and it is found that the signal of the six pairs of matched circles could be missed by current analyses of CMB sky maps.

astro-ph↗
arXiv2004

Can one hear the shape of the Universe?

It is shown that the recent observations of NASA's explorer mission "Wilkinson Microwave Anisotropy Probe" (WMAP) hint that our Universe may possess a non-trivial topology. As an example we discuss the Picard space which is stretched out into an infinitely long horn but with finite volume.

astro-ph↗
arXiv2003

Quintessence and the Curvature of the Universe after WMAP

We study quintessence models with a constant (effective) equation of state. It is investigated whether such quintessence models are consistent with a negative spatial curvature of the Universe with respect to the anisotropy of the cosmic microwave background radiation measured by the WMAP mission. If the reionization is negligibly small, it is found that such models with negative curvature are admissible due to a geometrical degeneracy. However, a very high optical depth tau to the surface of last scattering, as indicated by the polarization measurements of WMAP, would rule out such models.

astro-ph↗
arXiv2002

Quintessence with a constant equation of state in hyperbolic universes

Quintessence models leading to a constant equation of state are studied in hyperbolic universes. General properties of the quintessence potentials V(phi) are discussed, and for some special cases also the exact analytic expressions for these potentials are derived. It is shown that the observed angular power spectrum of the cosmic microwave background (CMB) is in excellent agreement with some of the quintessence models even in cases with negative curvature. It is emphasized that due to a (w_phi, Omega_phi, Omega_c)-degeneracy a universe with negative spatial curvature cannot be excluded.

astro-ph↗
arXiv2002

Behaviour of boundary functions for quantum billiards

We study the behaviour of the normal derivative of eigenfunctions of the Helmholtz equation inside billiards with Dirichlet boundary condition. These boundary functions are of particular importance because they uniquely determine the eigenfunctions inside the billiard and also other physical quantities of interest. Therefore they form a reduced representation of the quantum system, analogous to the Poincaré section of the classical system. For the normal derivatives we introduce an equivalent to the standard Green function and derive an integral equation on the boundary. Based on this integral equation we compute the first two terms of the mean asymptotic behaviour of the boundary functions for large energies. The first term is universal and independent of the shape of the billiard. The second one is proportional to the curvature of the boundary. The asymptotic behaviour is compared with numerical results for the stadium billiard, different limacon billiards and the circle billiard, and good agreement is found. Furthermore we derive an asymptotic completeness relation for the boundary functions.

nlin.CD↗
arXiv2002

Dark Energy in a Hyperbolic Universe

Dark energy models due to a slowly evolving scalar (quintessence) field $ϕ$ are studied for various potentials $V(ϕ)$ in a universe with negative curvature. The potentials differ in whether they possess a minimum at $ϕ=0$ or are monotonically declining, i.e. have a minimum at infinity. The angular power spectrum $C_l$ of the cosmic microwave background (CMB) as well as the magnitude-redshift relation $m_B(z)$ of the type Ia supernovae are compared with the quintessence models. It is demonstrated that some of the models with $Ω_tot \simeq 0.85...0.9$ are in agreement with the observations, i.e. possess acoustic peaks in the angular power spectrum of the CMB anisotropy as observed experimentally, and yield a magnitude-redshift relation in agreement with the data. Furthermore, it is found that the power spectrum $P(k)$ of the large-scale structure (LSS) agrees with the observations too.

astro-ph↗
arXiv2000

The Cosmic Microwave Background for a Nearly Flat Compact Hyperbolic Universe

The fluctuations of the cosmic microwave background (CMB) are investigated for a hyperbolic universe with finite volume. Four-component models with radiation, matter, vacuum energy, and an extra spatially constant dark energy X-component are considered. The general solution of the Friedmann equation for the cosmic scale factor a(eta) is given for the four-component models in terms of the Weierstrass P-function. The lower part of the angular power spectra C_l of the CMB anisotropy is computed for nearly flat models with Omega_tot <= 0.95. It is shown that the particular compact fundamental cell, which is considered in this paper, leads to a suppression in C_l for l<10 and Omega_tot <= 0.9.

astro-ph↗
arXiv1996

Mode fluctuations as fingerprint of chaotic and non-chaotic systems

The mode-fluctuation distribution $P(W)$ is studied for chaotic as well as for non-chaotic quantum billiards. This statistic is discussed in the broader framework of the $E(k,L)$ functions being the probability of finding $k$ energy levels in a randomly chosen interval of length $L$, and the distribution of $n(L)$, where $n(L)$ is the number of levels in such an interval, and their cumulants $c_k(L)$. It is demonstrated that the cumulants provide a possible measure for the distinction between chaotic and non-chaotic systems. The vanishing of the normalized cumulants $C_k$, $k\geq 3$, implies a Gaussian behaviour of $P(W)$, which is realized in the case of chaotic systems, whereas non-chaotic systems display non-vanishing values for these cumulants leading to a non-Gaussian behaviour of $P(W)$. For some integrable systems there exist rigorous proofs of the non-Gaussian behaviour which are also discussed. Our numerical results and the rigorous results for integrable systems suggest that a clear fingerprint of chaotic systems is provided by a Gaussian distribution of the mode-fluctuation distribution $P(W)$.

chao-dyn↗
arXiv1994

Spectral Statistics in the Quantized Cardioid Billiard

The spectral statistics in the strongly chaotic cardioid billiard are studied. The analysis is based on the first 11000 quantal energy levels for odd and even symmetry respectively. It is found that the level-spacing distribution is in good agreement with the GOE distribution of random-matrix theory. In case of the number variance and rigidity we observe agreement with the random-matrix model for short-range correlations only, whereas for long-range correlations both statistics saturate in agreement with semiclassical expectations. Furthermore the conjecture that for classically chaotic systems the normalized mode fluctuations have a universal Gaussian distribution with unit variance is tested and found to be in very good agreement for both symmetry classes. By means of the Gutzwiller trace formula the trace of the cosine-modulated heat kernel is studied. Since the billiard boundary is focusing there are conjugate points giving rise to zeros at the locations of the periodic orbits instead of exclusively Gaussian peaks.

chao-dyn↗
arXiv1994

On the Role of Non-Periodic Orbits in The Semiclassical Quantization of the Truncated Hyperbola Billiard

Based on an accurate computation of the first 1851 quantal energy levels of the truncated hyperbola billiard, we have found an anomalous long-range modulation in the integrated level density. It is shown that the observed anomaly can be explained by an additional term in Gutzwiller's trace formula. This term is given as a sum over families of closed, non-periodic orbits which are reflected in a point of the billiard boundary where the boundary is continuously differentiable, but its curvature radius changes discontinuously.

chao-dyn↗