CMB Anisotropy of the Poincaré Dodecahedron

The Poincaré Dodecahedral Space and the Mystery of the Missing Fluctuations, Volume 51, Number 6

Harmonic Polynomials on the Poincaré Dodecahedral Three-manifold

The global topology of the three-space is not fixed by Einstein general relativity, since this is formulated in terms of local differential equations. Einstein’s first static cosmological models used for the space-part of the universe a simply connected sphere S3. With present-day cosmological information it becomes possible to propose and test multiply-connected topologies for the space-part o...

Orbifold construction of the modes of the Poincaré dodecahedral space

We provide a new construction of the modes of the Poincaré dodecahedral space S3/I∗. The construction uses the Hopf map, Maxwell’s multipole vectors and orbifolds. In particular, the *235-orbifold serves as a parameter space for the modes of S3/I∗, shedding new light on the geometrical significance of the dimension of each space of k-modes, as well as on the modes themselves.

- qc / 0 70 10 17 v 1 1 J an 2 00 7 Harmonic polynomials for expanding the fluctuations of the Cosmic Microwave Background : The Poincaré and the 3 - sphere model

1 Abstract. Fluctuations of the Cosmic Microwave Background CMB are observed by the WMAP. When expanded into the harmonic eigenmodes of the space part of a cosmological model, they provide insight into the large-scale topology of space. All harmonic polynomials on the multiply connected dodecahedral Poincaré space are constructed. Strong and specific selection rules are given by comparing the p...

Skewness in the Cosmic Microwave Background Anisotropy from Inflationary Gravity Wave Background

In the context of inflationary scenarios, the observed large angle anisotropy of the Cosmic Microwave Background (CMB) temperature is believed to probe the primordial metric perturbations from inflation. Although the perturbations from inflation are expected to be gaussian random fields, there remains the possibility that nonlinear processes at later epochs induce “secondary” non-gaussian featu...