Forum for Science, Industry and Business

Sponsored by:     3M 
Search our Site:


The Poincaré Dodecahedral Space model gains support to explain the shape of space

An international team of cosmologists, leaded by a researcher from Paris Observatory, has improved the theoretical pertinence of the Poincaré Dodecahedral Space (PDS) topology to explain some observations of the Cosmic Microwave Background (CMB).

In parallel, another international team has analyzed with new techniques the last data obtained by the WMAP satellite and found a topological signal characteristic of the PDS geometry.

The last fifteen years have shown considerable growth in attempts to determine the global shape of the universe, i.e. not only the curvature of space but also its topology. The « concordance » cosmological model which now prevails describes the universe as a « flat » (zero-curvature) infinite space in eternal, accelerated expansion.

However, the data delivered between 2003 and 2006 by the NASA satellite WMAP, which produced a full-sky, high resolution map of the Cosmic Microwave Background Radiation (CMB), yield a very poor fit to the concordance model at large angular scales. They rather tend to favor a finite, positively curved space, and provide hints about a multiply-connected topology.

The CMB is the relics of the radiation emitted soon after the Big Bang. It is observed on the so-called last scattering surface (LSS), a sphere of radius about 50 billion light-years around us. The tiny temperature fluctuations observed on the LSS may be decomposed into a sum of spherical harmonics, much like the sound produced by a music instrument may be decomposed into ordinary harmonics. The relative amplitudes of each spherical harmonics determine the power spectrum, which is a signature of the geometry of space and of the physical conditions which prevailed at the time of CMB emission.

Now, cosmic topology predicts that a space which is smaller than the LSS cannot contain vibrational modes larger than the space itself. This should lead to a cutoff of power in statistics representing these fluctuations, above which power should drop to zero. The predicted cutoff in large scale power has precisely been observed by the 2003-2006 WMAP all-sky survey.

Motivated by indications that the Universe may have positive curvature, and calculating large-angle vibrational harmonics to simulate the power spectrum, some authors of the present study [ref. 2] had already argued in October 2003 that the multiply-connected Poincaré dodecahedral space (PDS) topology was favoured by the WMAP data relative to an infinite, simply connected flat space.

The PDS model has since been studied in more mathematical details by several teams all around the world. In the most recent study, Luminet and co-workers [ref. 1] calculated 1,7 billion vibrational modes of PDS to simulate more accurately the power spectrum, from large to small angular scales. They found that the maximal repression of the quadrupole signal, as found in the data, requires an optimal total density of Otot = 1.018 (see note 1). Their predicted PDS power spectrum then remarkably agrees with the observed one.

Circle signature

If physical space is smaller than the observed space inside the LSS sphere, there must be particular correlations in the CMB, namely pairs of « matched » circles along which temperature fluctuations should be the same, as they would represent the same physical points but observed from different directions due to topological lensing. As a definite signature of the underlying topology, the PDS model predicts six pairs of antipodal matched circles with a relative phase of 36°. To test this prediction, the team [ref.1] has simulated CMB temperature fluctuations maps in the PDS topology and checked the presence of the expected circles-in-the-sky.

Now the crucial question is : are these pairs of matched circles present in the real WMAP data ? Three different teams (from USA, Germany and Poland) have addressed the problem in the recent years, using various statistical indicators and massive computer calculations. No clear answer presently emerges, because the expected positive correlation signal from matched pairs is spoiled by various cosmological effects, astrophysical foregrounds and instrumental effects that constitute noise.

Thus, another international team of cosmologists [ref. 3] lead by B. Roukema of Torun University in Poland (formerly at Paris-Meudon Observatory), has reanalyzed the WMAP data with new statistical tools. They have shown that cross-correlations of temperature fluctuations on multiple copies of the LSS imply a highly cross-correlated PDS symmetry with the correct phase of 36° for the matched circles. By determining the position of such circles, they were even able to fix the space orientation of the fundamental dodecahedron relative to the CMB frame.


Do we really live in a Poincaré Dodecahedral Space? Further constraints either for or against the model are certainly still needed, but the evidence in favour of a PDS-like signal in the WMAP data does seem to be cumulating. To clarify the issue, new data from the future European satellite Planck Surveyor (launch scheduled in july 2008) are eagerly expected.

Note 1
The mass-energy density parameter Otot characterizes the contents (matter and all forms of energy) of the universe. The curvature of space depends on the value of this parameter. If Otot is greater than 1, then space curvature is positive and geometry is spherical; if Otot is smaller than 1 the curvature is negative and the geometry is hyperbolic; eventually Otot is strictly equal to 1 and space is Euclidian.

Jean-Pierre Luminet | alfa
Further information:

More articles from Physics and Astronomy:

nachricht SwRI-led team discovers lull in Mars' giant impact history
26.04.2017 | Southwest Research Institute

nachricht New survey hints at exotic origin for the Cold Spot
26.04.2017 | Royal Astronomical Society

All articles from Physics and Astronomy >>>

The most recent press releases about innovation >>>

Die letzten 5 Focus-News des innovations-reports im Überblick:

Im Focus: Making lightweight construction suitable for series production

More and more automobile companies are focusing on body parts made of carbon fiber reinforced plastics (CFRP). However, manufacturing and repair costs must be further reduced in order to make CFRP more economical in use. Together with the Volkswagen AG and five other partners in the project HolQueSt 3D, the Laser Zentrum Hannover e.V. (LZH) has developed laser processes for the automatic trimming, drilling and repair of three-dimensional components.

Automated manufacturing processes are the basis for ultimately establishing the series production of CFRP components. In the project HolQueSt 3D, the LZH has...

Im Focus: Wonder material? Novel nanotube structure strengthens thin films for flexible electronics

Reflecting the structure of composites found in nature and the ancient world, researchers at the University of Illinois at Urbana-Champaign have synthesized thin carbon nanotube (CNT) textiles that exhibit both high electrical conductivity and a level of toughness that is about fifty times higher than copper films, currently used in electronics.

"The structural robustness of thin metal films has significant importance for the reliable operation of smart skin and flexible electronics including...

Im Focus: Deep inside Galaxy M87

The nearby, giant radio galaxy M87 hosts a supermassive black hole (BH) and is well-known for its bright jet dominating the spectrum over ten orders of magnitude in frequency. Due to its proximity, jet prominence, and the large black hole mass, M87 is the best laboratory for investigating the formation, acceleration, and collimation of relativistic jets. A research team led by Silke Britzen from the Max Planck Institute for Radio Astronomy in Bonn, Germany, has found strong indication for turbulent processes connecting the accretion disk and the jet of that galaxy providing insights into the longstanding problem of the origin of astrophysical jets.

Supermassive black holes form some of the most enigmatic phenomena in astrophysics. Their enormous energy output is supposed to be generated by the...

Im Focus: A Quantum Low Pass for Photons

Physicists in Garching observe novel quantum effect that limits the number of emitted photons.

The probability to find a certain number of photons inside a laser pulse usually corresponds to a classical distribution of independent events, the so-called...

Im Focus: Microprocessors based on a layer of just three atoms

Microprocessors based on atomically thin materials hold the promise of the evolution of traditional processors as well as new applications in the field of flexible electronics. Now, a TU Wien research team led by Thomas Müller has made a breakthrough in this field as part of an ongoing research project.

Two-dimensional materials, or 2D materials for short, are extremely versatile, although – or often more precisely because – they are made up of just one or a...

All Focus news of the innovation-report >>>



Event News

Expert meeting “Health Business Connect” will connect international medical technology companies

20.04.2017 | Event News

Wenn der Computer das Gehirn austrickst

18.04.2017 | Event News

7th International Conference on Crystalline Silicon Photovoltaics in Freiburg on April 3-5, 2017

03.04.2017 | Event News

Latest News

Scientist invents way to trigger artificial photosynthesis to clean air

26.04.2017 | Materials Sciences

Ammonium nitrogen input increases the synthesis of anticarcinogenic compounds in broccoli

26.04.2017 | Agricultural and Forestry Science

SwRI-led team discovers lull in Mars' giant impact history

26.04.2017 | Physics and Astronomy

More VideoLinks >>>