Forum for Science, Industry and Business

Sponsored by:     3M 
Search our Site:

 

Vibrations of the Cosmic Drumhead

06.01.2003


A multiconnected topology translates into the fact that any object in space may possess several copies of itself in the observable Universe. For an extended object like the region of emission of the CMB radiation we observe (the so-called last scattering surface) it can happen that it intersects with itself along pairs of circles [5]. In this case;; this is equivalent to say that an observer (located at the center of the last scattering surface) will see the same region of the Universe from different directions. As a consequence;; the temperature fluctuations will match along the intersection of the last scattering surface with itself;; as illustrated in the above figure. This CMP map is simulated for a multi-connected flat space - namely a cubic hypertorus whose length is 3.17 times smaller than the diameter of the last scattering surface.


Cosmologists hope to "hear the shape of space", namely its topology, by analyzing in detail the temperature fluctuations in the cosmic microwave background radiation (CMB). An international team of cosmologists, including researchers from l’Observatoire de Paris, has recently developped a model for the vibrations of the universe. For the first time [1], they have simulated high resolution CMB maps containing the signatures of a wide class of topologies, for comparison with the forthcoming MAP satellite data in early 2003.

The shape of space

In recent years, cosmologists have become interested in the global shape of space [2]. Previously, most of them had neglected the fact that, even if space is flat on a large scale, it can take many different shapes, for instance that of a doughnut-like hypertorus. A space of a given curvature admits a number a topologies. Indeed, 18 flat topologies along with an infinite number of spherical and hyperbolic ones are theoretical candidates to describe the shape of physical space.



Although recent CMB observations constrain the value of space curvature to a very narrow range about zero, they still leave open the question of whether the average curvature is exactly zero (corresponding to a flat universe) slightly positive (spherical universe) or slightly negative (hyperbolic universe), and above all whether the topology is simple (for instance an infinite flat space) or not (for instance a finite flat hypertorus).
In a previous article [3], three authors have proved that the spherical topologies would be more easily detectable observationally than hyperbolic or flat ones. The reason is that, no matter how close space is to perfect flatness, only a finite number of spherical shapes are excluded by observational constraints. Due to the special structure of spherical spaces, topological imprints would be potentially detectable within the observable universe. Thus cosmologists are taking a renewed interest in spherical spaces as possible models for the physical universe. Now the main question is : how to detect the topology of space?

The Universe as a drumhead

If you sprinkle fine sand uniformly over a drumhead and then make it vibrate, the grains of sand will collect in characteristic spots and figures, called Chladni patterns. These patterns reveal much information about the size and the shape of the drum and the elasticity of its membrane. In particular, the distribution of spots depends not only on the way the drum vibrated initially but also on the global shape of the drum, because the waves will be reflected differently according to whether the edge of the drumhead is a circle, an ellipse, a square, or some other shape.

In cosmology, the early Universe was crossed by real acoustic waves generated soon after Big Bang. Such vibrations left their imprints 300 000 years later as tiny density fluctuations in the primordial plasma. Hot and cold spots in the present-day 2.7 K CMB radiation reveal those density fluctuations. Thus the CMB temperature fluctuations look like Chladni patterns resulting from a complicated three-dimensional drumhead that vibrated for 300 000 years. They yield a wealth of information about the physical conditions that prevailed in the early Universe, as well as present geometrical properties like space curvature and topology. More precisely, density fluctuations may be expressed as combinations of the vibrational modes of space, just as the vibration of a drumhead may be expressed as a combination of the drumhead’s harmonics.

For the first time, a team of physicists has shown how the shape of a spherical space can be heard in a unique way. They calculated the harmonics (the so-called "eigenmodes of the Laplace operator") for most of the spherical topologies [4]. Next, starting from a set of initial conditions fixing how the universe originally vibrated (the so-called Harrison-Zeldovich spectrum), they evolved the harmonics forward in time to simulate realistic CMB maps for a number of topologies, including flat and spherical ones [1].

Waiting for the data

Balloon-borne CMB experiments (Boomerang, DASI, Archeops) have put tight constraints on the curvature of space, but provide too little data to test the topology of the Universe because they cover only a small portion of the sky. The situation is about to change dramatically with the MAP (Microwave Anisotropy Probe) satellite mission.

Launched by NASA in April, 2001, it will provide high resolution maps of CMB fluctuations on the whole sky, excluding the portion obscured by our own Milky Way galaxy. The 6-month MAP data will be released late January or early February 2003. A topological signal as predicted in [5], and simulated in the maps of [1], may be subtly encoded in these data, and may eventually answer the fascinating question whether space is finite.


Peer reviewed publications and references

[1] A. Riazuelo, J.-P. Uzan, R. Lehoucq and J. Weeks, "Simulating Cosmic microwave background maps in multi-connected universes" (e-print astro-ph/0212223).

[2] J.- P. Luminet: "L’Univers chiffonné", Fayard, Paris, 2001, 369 p.
R. Lehoucq: "L’univers a-t-il une forme ?", Flammarion, Paris 2002, 152 p.
J. Weeks : "The Shape of Space", Dekker, 2nd edition, 2001, 328 p.

[3] J. Weeks, R. Lehoucq and J.-P. Uzan: "Detecting topology in a Nearly Flat Spherical Universe", (e-print astro-ph/0209389).

[4] R. Lehoucq, J. Weeks, J.-P. Uzan, E. Gausmann and J.-P. Luminet, "Eigenmodes of 3-dimensional spherical spaces and their application to cosmology", Classical and
Quantum Gravity,(2002) 19, 4683-4708 (e-print gr-qc/0205009).

[5] N. Cornish, D. Spergel and G. Starkman,"Circles in the sky: finding topology with the microwave background radiation", Classical and Quantum Gravity (1998), 15,
2657-2670 (e-print astro-ph/9801212).

Jean-Pierre Luminet | alfa
Further information:
http://luth2.obspm.fr/Compress/jan03_riaz.en.html

More articles from Physics and Astronomy:

nachricht NASA spacecraft investigate clues in radiation belts
28.03.2017 | NASA/Goddard Space Flight Center

nachricht Researchers create artificial materials atom-by-atom
28.03.2017 | Aalto University

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: A Challenging European Research Project to Develop New Tiny Microscopes

The Institute of Semiconductor Technology and the Institute of Physical and Theoretical Chemistry, both members of the Laboratory for Emerging Nanometrology (LENA), at Technische Universität Braunschweig are partners in a new European research project entitled ChipScope, which aims to develop a completely new and extremely small optical microscope capable of observing the interior of living cells in real time. A consortium of 7 partners from 5 countries will tackle this issue with very ambitious objectives during a four-year research program.

To demonstrate the usefulness of this new scientific tool, at the end of the project the developed chip-sized microscope will be used to observe in real-time...

Im Focus: Giant Magnetic Fields in the Universe

Astronomers from Bonn and Tautenburg in Thuringia (Germany) used the 100-m radio telescope at Effelsberg to observe several galaxy clusters. At the edges of these large accumulations of dark matter, stellar systems (galaxies), hot gas, and charged particles, they found magnetic fields that are exceptionally ordered over distances of many million light years. This makes them the most extended magnetic fields in the universe known so far.

The results will be published on March 22 in the journal „Astronomy & Astrophysics“.

Galaxy clusters are the largest gravitationally bound structures in the universe. With a typical extent of about 10 million light years, i.e. 100 times the...

Im Focus: Tracing down linear ubiquitination

Researchers at the Goethe University Frankfurt, together with partners from the University of Tübingen in Germany and Queen Mary University as well as Francis Crick Institute from London (UK) have developed a novel technology to decipher the secret ubiquitin code.

Ubiquitin is a small protein that can be linked to other cellular proteins, thereby controlling and modulating their functions. The attachment occurs in many...

Im Focus: Perovskite edges can be tuned for optoelectronic performance

Layered 2D material improves efficiency for solar cells and LEDs

In the eternal search for next generation high-efficiency solar cells and LEDs, scientists at Los Alamos National Laboratory and their partners are creating...

Im Focus: Polymer-coated silicon nanosheets as alternative to graphene: A perfect team for nanoelectronics

Silicon nanosheets are thin, two-dimensional layers with exceptional optoelectronic properties very similar to those of graphene. Albeit, the nanosheets are less stable. Now researchers at the Technical University of Munich (TUM) have, for the first time ever, produced a composite material combining silicon nanosheets and a polymer that is both UV-resistant and easy to process. This brings the scientists a significant step closer to industrial applications like flexible displays and photosensors.

Silicon nanosheets are thin, two-dimensional layers with exceptional optoelectronic properties very similar to those of graphene. Albeit, the nanosheets are...

All Focus news of the innovation-report >>>

Anzeige

Anzeige

Event News

International Land Use Symposium ILUS 2017: Call for Abstracts and Registration open

20.03.2017 | Event News

CONNECT 2017: International congress on connective tissue

14.03.2017 | Event News

ICTM Conference: Turbine Construction between Big Data and Additive Manufacturing

07.03.2017 | Event News

 
Latest News

Transport of molecular motors into cilia

28.03.2017 | Life Sciences

A novel hybrid UAV that may change the way people operate drones

28.03.2017 | Information Technology

NASA spacecraft investigate clues in radiation belts

28.03.2017 | Physics and Astronomy

VideoLinks
B2B-VideoLinks
More VideoLinks >>>