13.10.2003

A franco-american quintet of cosmologists conducted by Jean-Pierre Luminet, from Paris Observatory (LUTH), has proposed an original explanation to account for a surprising detail observed in the Cosmic Microwave Background (CMB) recently mapped by the NASA satellite WMAP. According to the team, who published their study in the 9 october 2003 issue of "Nature", an intriguing discrepancy in the background luminous texture of the Universe can indeed be explained by a very specific global shape of space (its "topology"). The Universe could be wrapped around, a little bit like a "soccer ball", the volume of which would represent only 80% of the observable Universe! According to the leading cosmologist George Ellis, from Cape Town University (South Africa), who comments this letter in the "News & Views" of the same issue: "If confirmed, it is a major discovery about the nature of the Universe".

**Primordial fluctuations**

Cosmologists study the topology of space by analyzing in great details the temperature fluctuations of the fossil Cosmic Microwave Background [note a]. The standard cosmological model describes the Universe as a flat infinite space in eternal, accelerated expansion under the effect of a repulsive "dark energy". The data collected by the NASA satellite WMAP (Wilkinson Microwave Anisotropy Probe), which has recently produced a high resolution map of the CMB, allowed to check the validity of such an expansion model. Temperature fluctuations on small and mean scales (i.e. concerning regions of the sky of relatively modest size) are compatible with the infinite flat space hypothesis. However, on angular scales larger than 60°, the observed correlations are notably weaker that those predicted by the standard model. Thus the scientists are looking for an alternative.

CMB temperature anisotropies essentially result from density fluctuations of the primordial Universe : a photon coming from a denser region will loose a fraction of its energy to compete against gravity, and will reach us cooler. On the contrary, photons emitted from less dense regions will be received hotter. The density fluctuations result from the superposition of acoustic waves which propagated in the primordial plasma - see previous AlphaGalileo press releases "Vibrations of the cosmic drumhead" (6 jan 03) and "A small spherical Universe?" (12 nov 01).

The franco-american team of scientists has recently developed complex theoretical models to reproduce the amplitude of such fluctuations, which can be considered as vibrations of the Universe itself. In particular, they simulated high resolution CMB maps for various space topologies and were able to compare their results with real WMAP data. Depending on the underlying topology, the distribution of the fluctuations differs. For instance, in an infinite "flat" (Euclidean) space, all wavelengths are allowed, and fluctuations must be present at all scales.

Like acoustic waves, the CMB temperature fluctuations can be decomposed into a sum of spherical harmonics [note b]. The first observable harmonics is the quadrupole (whose wavenumer is l=2). WMAP has observed a value of the quadrupole 7 times weaker than expected in a flat infinite Universe. The probability that such a discrepancy occurs by chance has been estimated to 0.2% only. The octopole (whose wavenumber is l=3) is also weaker (72%) than the expected value. For larger wavenumbers up to l=900 (which correspond to temperature fluctuations at small angular scales), observations are remarkably consistent with the standard cosmological model.

The unusually low quadrupole value means that long wavelengths are missing, may be because space is not big enough to sustain them. Such a situation may be compared to a vibraring string fixed at its two extremities, for which the maximum wavelength of an oscillation is twice the string length. A natural explanation of such a phenomenon relies on a model of finite space whose size constrains the wavelengths below a maximum value. The proposed space is the Poincaré dodecahedral space [note c].

The associated power spectrum, namely the repartition of fluctuations as a function of their wavelengths corresponding to the Poincaré dodecahedral space, strongly depends on the value of the mass-energy density parameter [note d]. There is a small interval of values within which the spectral fit is good, and in agreement with the value of the density parameter deduced from WMAP data (1.02 plus or minus 0.02). The result is quite remarkable because the Poincaré space has no degree of freedom. By contrast, a 3-dimensional torus, constructed by gluing together the opposite faces of a cube and which constitutes a possible topology for a finite Euclidean space, may be deformed into any parallelepiped : therefore its geometrical construction depends on 6 degrees of freedom.

The Poincaré Dodecahedral Space accounts for the low value of the quadrupole as observed by WMAP in the fluctuation spectrum, and provides a good value of the octopole. To be confirmed, such a "soccer-ball" model of space must satisfy two experimental tests :

1) A finer analysis of WMAP data, or new data from the future European satellite "Planck Surveyor" (scheduled 2007), will be able to determine the value of the energy density parameter with a precision of 1%. A value lower than 1.01 will discard the Poincaré space as a model for cosmic space, whereas a value greater than 1.01 will confirm its cosmological pertinence.

2) If space has a non trivial topology, there must be particular correlations in the CMB, namely pairs of correlated circles along which temperature fluctuations should be the same. The Poincaré Dodecahedral Space model predicts 6 pairs of circles with an angular radius of 35°. The model is therefore an ideal candidate to test the method of "matched circles" originally devised by the American astrophysicists N. Cornish, D. Spergel and G. Starkman

[a] The Cosmic Background Radiation, also called Fossil Radiation, is the relics of the radiation emitted soon after the Big Bang (about 400 000 years later), when matter and radiation decoupled. The tiny temperature irregularities of such a radiation allow to measure the density fluctuations of the matter present at this epoch, such fluctuations being the seeds of all galaxies and galaxy clusters.

[b] The temperature fluctuations of the Cosmic Background Radiation 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 "fundamental" fixes the height of the note (as for instance a 440 hertz acoustic frequency fixes the "A" of the pitch), whereas the relative amplitudes of each harmonics determine the tone quality (such as the A played by a piano differs from the A played by a harpsichord). Concerning the relic radiation, 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.

[c] Poincaré space may be represented by a dodecahedron (a regular polyhedron with 12 pentagonal faces) whose opposite faces are glued after a 36° twist ; such a space is positively curved, and is a multiply connected variant of the hypersphere, with a volume 120 times smaller. A rocket going out of the dodecahedron by crossing a given face immediately re-enters by the opposite face. Propagation of light rays is such that any observer whose line-of-sight intercepts one face has the illusion to see inside a copy of his own dodecahedron (since his line-of-sight re-enters the original dodecahedron from the opposite side).

[d] The mass-energy density parameter characterizes the contents (matter and all forms of energy) of the Universe. The curvature of space depends on the value of this parameter, usually denoted Omega. If Omega is greater than 1, then space curvature is positive and geometry is spherical; if Omega is smaller than 1 the curvature is negative and the geometry is hyperbolic; eventually Omega is strictly equal to 1 and space is "flat" (Euclidean geometry).

Jean-Pierre Luminet | alfa

Further information:

http://luth2.obspm.fr/Compress/oct03_lum.en.html

Measured for the first time: Direction of light waves changed by quantum effect

24.05.2017 | Vienna University of Technology

Physicists discover mechanism behind granular capillary effect

24.05.2017 | University of Cologne

Physicists from the University of Würzburg are capable of generating identical looking single light particles at the push of a button. Two new studies now demonstrate the potential this method holds.

The quantum computer has fuelled the imagination of scientists for decades: It is based on fundamentally different phenomena than a conventional computer....

An international team of physicists has monitored the scattering behaviour of electrons in a non-conducting material in real-time. Their insights could be beneficial for radiotherapy.

We can refer to electrons in non-conducting materials as ‘sluggish’. Typically, they remain fixed in a location, deep inside an atomic composite. It is hence...

Two-dimensional magnetic structures are regarded as a promising material for new types of data storage, since the magnetic properties of individual molecular building blocks can be investigated and modified. For the first time, researchers have now produced a wafer-thin ferrimagnet, in which molecules with different magnetic centers arrange themselves on a gold surface to form a checkerboard pattern. Scientists at the Swiss Nanoscience Institute at the University of Basel and the Paul Scherrer Institute published their findings in the journal Nature Communications.

Ferrimagnets are composed of two centers which are magnetized at different strengths and point in opposing directions. Two-dimensional, quasi-flat ferrimagnets...

An Australian-Chinese research team has created the world's thinnest hologram, paving the way towards the integration of 3D holography into everyday...

In the race to produce a quantum computer, a number of projects are seeking a way to create quantum bits -- or qubits -- that are stable, meaning they are not much affected by changes in their environment. This normally needs highly nonlinear non-dissipative elements capable of functioning at very low temperatures.

In pursuit of this goal, researchers at EPFL's Laboratory of Photonics and Quantum Measurements LPQM (STI/SB), have investigated a nonlinear graphene-based...

Anzeige

Anzeige

Event News

Marine Conservation: IASS Contributes to UN Ocean Conference in New York on 5-9 June

24.05.2017 | Event News

AWK Aachen Machine Tool Colloquium 2017: Internet of Production for Agile Enterprises

23.05.2017 | Event News

Dortmund MST Conference presents Individualized Healthcare Solutions with micro and nanotechnology

22.05.2017 | Event News

Latest News

Physicists discover mechanism behind granular capillary effect

24.05.2017 | Physics and Astronomy

Measured for the first time: Direction of light waves changed by quantum effect

24.05.2017 | Physics and Astronomy

Marine Conservation: IASS Contributes to UN Ocean Conference in New York on 5-9 June

24.05.2017 | Event News

VideoLinks

NASA | A Year in the Life of Earth's CO2

NASA Computer Model Provides a New Portrait of Carbon Dioxide

Black Holes Come to the Big Screen

The new movie "Interstellar" explores a longstanding fascination, but UA astrophysicists are using cutting-edge technology to go one better.

NASA's Swift Mission Observes Mega Flares from a Mini Star

NASA's Swift satellite detected the strongest, hottest, and longest-lasting sequence of stellar flares ever seen from a nearby red dwarf star.

NASA | Global Hawks Soar into Storms

NASA's airborne Hurricane and Severe Storm Sentinel or HS3 mission, will revisit the Atlantic Ocean for the third year in a row.

Baffin Island - Disappearing ice caps

Giff Miller, geologist and paleoclima-tologist, is walking the margins of melting glaciers on Baffin Island, Nunavut, Canada.

The Infrasound Network and how it works

The CTBTO uses infrasound stations to monitor the Earth mainly for atmospheric explosions.

B2B-VideoLinks

Efficient reduction of odour and grease with Heraeus UV solutions

Kitchen exhaust air cleaning with UV in gastronomy

Drying and curing of paints on glass and ceramics

Bright and brilliant paints on glass and ceramics require safe solutions for drying and curing.

JULABO World of Temperature

Explore the World of Temperature with JULABO - Superior Temperature Technology for a Better Life.

Acoustic Wave Separation: How It Works

In this animated video, see how Acoustic Wave Separation technology works in full detail.

Infrared Heat for printed electronics

Drying and sintering of printed electronics by specialty light sources from Heraeus

All about Data Logger, how to use

Wolfgang Rudolph explains: all information worth knowing about the data logger and the practical test by means of a drone