Eigenmodes of three-dimensional spherical spaces and their application to cosmology

  title={Eigenmodes of three-dimensional spherical spaces and their application to cosmology},
  author={Roland Lehoucq and Jeffrey R. Weeks and Jean-Philippe Uzan and Evelise Gausmann and Jean-Pierre Luminet},
  journal={Classical and Quantum Gravity},
This paper investigates the computation of the eigenmodes of the Laplacian operator in multi-connected three-dimensional spherical spaces. General mathematical results and analytical solutions for lens and prism spaces are presented. Three complementary numerical methods are developed and compared with our analytic results and previous investigations. The cosmological applications of these results are discussed, focusing on the cosmic microwave background (CMB) anisotropies. In particular… 
Eigenmodes of dodecahedral space
Cosmological models wherein spatial sections are the Poincare dodecahedral space D have been recently invoked to explain the missing power in the low-order angular modes of the cosmic microwave
Laplacian eigenmodes for spherical spaces
The possibility that our space is multi–rather than singly–connected has gained renewed interest after the discovery of the low power for the first multipoles of the CMB by WMAP. To test the
Exact polynomial eigenmodes for homogeneous spherical 3-manifolds
Observational data hint at a finite universe, with spherical manifolds such as the Poincare dodecahedral space tentatively providing the best fit. Simulating the physics of a model universe requires
CMB radiation in an inhomogeneous spherical space
Abstract. We analyse the CMB radiation in spherical 3-spaces with non-trivial topology. The focus is put on an inhomogeneous space which possesses observer dependent CMB properties. The suppression
Spherical Universe topology and the Casimir effect
Recent interest in the possible non-trivial topology of the Universe, and the resulting analysis of the Laplacian eigenproblem, has prompted a reprise of calculations done by ourselves some time ago.
Cosmic microwave background radiation in an inhomogeneous spherical space
We analyse the cosmic microwave background (CMB) radiation in spherical three-spaces with nontrivial topology. The focus is on an inhomogeneous space which possesses observer-dependent CMB
CMB anisotropy of the poincaré dodecahedron
We analyse the anisotropy of the cosmic microwave background (CMB) for the Poincare dodecahedron which is an example of a multi-connected spherical universe. We compare the temperature correlation
The Spectral Action and Cosmic Topology
The spectral action functional, considered as a model of gravity coupled to matter, provides, in its non-perturbative form, a slow-roll potential for inflation, whose form and corresponding slow-roll
Platonic topology and CMB fluctuations: homotopy, anisotropy and multipole selection rules
The cosmic microwave background (CMB) originates from an early stage in the history of the universe. Observations show low-multipole contributions of CMB fluctuations. A possible explanation is given
Cosmic microwave background anisotropies in multiconnected flat spaces
This article investigates the signature of the seventeen multiconnected flat spaces in cosmic microwave background (CMB) maps. For each such space it recalls a fundamental domain and a set of


Computation of eigenmodes on a compact hyperbolic 3-space
Measurements of cosmic microwave background (CMB) anisotropy are ideal experiments for discovering the non-trivial global topology of the universe. To evaluate the CMB anisotropy in
Computing CMB anisotropy in compact hyperbolic spaces
The measurements of CMB anisotropy have opened up a window for probing the global topology of the universe on length scales comparable to and beyond the Hubble radius. For compact topologies, the two
Topological lensing in spherical spaces
This paper gives the construction and complete classification of all three-dimensional spherical manifolds and orders them by decreasing volume, in the context of multi-connected universe models with
CMB anisotropy in compact hyperbolic universes. I. Computing correlation functions
Cosmic microwave background ~CMB! anisotropy measurements have brought the issue of global topology of the universe from the realm of theoretical possibility to within the grasp of observations. The
Topological lens effects in universes with non-euclidean compact spatial sections
Universe models with compact spatial sections smaller than the observable universe produce a topological lens effect. Given a catalog of cosmic sources, we estimate the num- ber of topological images
The Fluctuations of the Cosmic Microwave Background for a Compact Hyperbolic Universe
The fluctuations of the cosmic microwave background (CMB) are investigated for a small, open universe, i.e., one that is periodically composed of a small fundamental cell. The evolution of initial
Geometric Gaussianity and non-Gaussianity in the cosmic microwave background
In this paper, the Gaussianity of eigenmodes and non-Gaussianity in the cosmic microwave background (CMB) temperature fluctuations in the two smallest compact hyperbolic (CH) models are investigated.
COBE constraints on a compact toroidal low-density universe
In this paper, the cosmic microwave background (CMB) anisotropy in a multiply connected compact flat 3-torus model with the cosmological constant is investigated. Using the COBE-DMR four-year data, a
A General, Gauge Invariant Analysis of the Cosmic Microwave Anisotropy
A general, gauge-invariant analysis of the large-scale anisotropies in the cosmic background radiation produced by arbitrary scalar, vector, or tensor perturbations in open, closed, or flat