432 research outputs found
Cosmic Topology of Polyhedral Double-Action Manifolds
A special class of non-trivial topologies of the spherical space S^3 is
investigated with respect to their cosmic microwave background (CMB)
anisotropies. The observed correlations of the anisotropies on the CMB sky
possess on large separation angles surprising low amplitudes which might be
naturally be explained by models of the Universe having a multiconnected
spatial space. We analysed in CQG 29(2012)215005 the CMB properties of prism
double-action manifolds that are generated by a binary dihedral group D^*_p and
a cyclic group Z_n up to a group order of 180. Here we extend the CMB analysis
to polyhedral double-action manifolds which are generated by the three binary
polyhedral groups (T^*, O^*, I^*) and a cyclic group Z_n up to a group order of
1000. There are 20 such polyhedral double-action manifolds. Some of them turn
out to have even lower CMB correlations on large angles than the Poincare
dodecahedron
How well-proportioned are lens and prism spaces?
The CMB anisotropies in spherical 3-spaces with a non-trivial topology are
analysed with a focus on lens and prism shaped fundamental cells. The
conjecture is tested that well proportioned spaces lead to a suppression of
large-scale anisotropies according to the observed cosmic microwave background
(CMB). The focus is put on lens spaces L(p,q) which are supposed to be oddly
proportioned. However, there are inhomogeneous lens spaces whose shape of the
Voronoi domain depends on the position of the observer within the manifold.
Such manifolds possess no fixed measure of well-proportioned and allow a
predestined test of the well-proportioned conjecture. Topologies having the
same Voronoi domain are shown to possess distinct CMB statistics which thus
provide a counter-example to the well-proportioned conjecture. The CMB
properties are analysed in terms of cyclic subgroups Z_p, and new point of view
for the superior behaviour of the Poincar\'e dodecahedron is found
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.Comment: 20 pages, uu-encoded ps.Z-fil
Cosmic microwave anisotropies in an inhomogeneous compact flat universe
The anisotropies of the cosmic microwave background (CMB) are computed for
the half-turn space E_2 which represents a compact flat model of the Universe,
i.e. one with finite volume. This model is inhomogeneous in the sense that the
statistical properties of the CMB depend on the position of the observer within
the fundamental cell. It is shown that the half-turn space describes the
observed CMB anisotropies on large scales better than the concordance model
with infinite volume. For most observer positions it matches the temperature
correlation function even slightly better than the well studied 3-torus
topology
Level spacings and periodic orbits
Starting from a semiclassical quantization condition based on the trace
formula, we derive a periodic-orbit formula for the distribution of spacings of
eigenvalues with k intermediate levels. Numerical tests verify the validity of
this representation for the nearest-neighbor level spacing (k=0). In a second
part, we present an asymptotic evaluation for large spacings, where consistency
with random matrix theory is achieved for large k. We also discuss the relation
with the method of Bogomolny and Keating [Phys. Rev. Lett. 77 (1996) 1472] for
two-point correlations.Comment: 4 pages, 2 figures; major revisions in the second part, range of
validity of asymptotic evaluation clarifie
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
The optimal phase of the generalised Poincare dodecahedral space hypothesis implied by the spatial cross-correlation function of the WMAP sky maps
Several studies have proposed that the shape of the Universe may be a
Poincare dodecahedral space (PDS) rather than an infinite, simply connected,
flat space. Both models assume a close to flat FLRW metric of about 30% matter
density. We study two predictions of the PDS model. (i) For the correct model,
the spatial two-point cross-correlation function, \ximc, of temperature
fluctuations in the covering space, where the two points in any pair are on
different copies of the surface of last scattering (SLS), should be of a
similar order of magnitude to the auto-correlation function, \xisc, on a
single copy of the SLS. (ii) The optimal orientation and identified circle
radius for a "generalised" PDS model of arbitrary twist , found by
maximising \ximc relative to \xisc in the WMAP maps, should yield . We optimise the cross-correlation at scales < 4.0 h^-1 Gpc
using a Markov chain Monte Carlo (MCMC) method over orientation, circle size
and . Both predictions were satisfied: (i) an optimal "generalised" PDS
solution was found, with a strong cross-correlation between points which would
be distant and only weakly correlated according to the simply connected
hypothesis, for two different foreground-reduced versions of the WMAP 3-year
all-sky map, both with and without the kp2 Galaxy mask: the face centres are
\phi
\in [0,2\pi]$, is about 6-9%.Comment: 20 pages, 22 figures, accepted in Astronomy & Astrophysics, software
available at http://adjani.astro.umk.pl/GPLdownload/dodec/ and MCMCs at
http://adjani.astro.umk.pl/GPLdownload/MCM
A measure on the set of compact Friedmann-Lemaitre-Robertson-Walker models
Compact, flat Friedmann-Lemaitre-Robertson-Walker (FLRW) models have recently
regained interest as a good fit to the observed cosmic microwave background
temperature fluctuations. However, it is generally thought that a globally,
exactly-flat FLRW model is theoretically improbable. Here, in order to obtain a
probability space on the set F of compact, comoving, 3-spatial sections of FLRW
models, a physically motivated hypothesis is proposed, using the density
parameter Omega as a derived rather than fundamental parameter. We assume that
the processes that select the 3-manifold also select a global mass-energy and a
Hubble parameter. The inferred range in Omega consists of a single real value
for any 3-manifold. Thus, the obvious measure over F is the discrete measure.
Hence, if the global mass-energy and Hubble parameter are a function of
3-manifold choice among compact FLRW models, then probability spaces
parametrised by Omega do not, in general, give a zero probability of a flat
model. Alternatively, parametrisation by the injectivity radius r_inj ("size")
suggests the Lebesgue measure. In this case, the probability space over the
injectivity radius implies that flat models occur almost surely (a.s.), in the
sense of probability theory, and non-flat models a.s. do not occur.Comment: 19 pages, 4 figures; v2: minor language improvements; v3:
generalisation: m, H functions of
Cosmic Topology of Prism Double-Action Manifolds
The cosmic microwave background (CMB) anisotropies in spherical 3-spaces with
a non-trivial topology are studied. This paper discusses the special class of
the so-called double-action manifolds, which are for the first time analysed
with respect to their CMB anisotropies. The CMB anisotropies are computed for
all prism double-action manifolds generated by a binary dihedral and a cyclic
group with a group order of up to 180 leading to 33 different topologies.
Several spaces are found which show a suppression of the CMB anisotropies on
large angular distances as it is found on the real CMB sky. It turns out that
two of these spaces possess Dirichlet domains which are not very far from
highly symmetric polyhedra like Platonic or Archimedean ones
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