Shape of the Universe

Shape of the Universe



From The Status of Cosmic Topology after Planck Data

In the last decade, the study of the overall shape of the universe, called Cosmic Topology, has become testable by astronomical observations, especially the data from the Cosmic Microwave Background (hereafter CMB) obtained by WMAP and Planck telescopes. Cosmic Topology involves both global topological features and more local geometrical properties such as curvature. It deals with questions such as whether space is finite or infinite, simply connected or multi connected, and smaller or greater than its observable counterpart. A striking feature of some relativistic, multi ­connected small universe models is to create multiples images of faraway cosmic sources. While the last CMB (Planck) data fit well the simplest model of a zero curvature, infinite space model, they remain consistent with more complex shapes such as the spherical Poincaré Dodecahedral Space, the flat hypertorus or the hyperbolic Picard horn.

From The Status of Cosmic Topology after Planck Data

The overall topology of the universe has become an important concern in astronomy and cosmology. Even if particularly simple and elegant models such as the PDS and the hypertorus are now claimed to be ruled out at a subhorizon scale, many more complex models of multi-­connected space cannot be eliminated as such. In addition, even if the size of a multi-­connected space is larger (but not too much) than that of the observable universe, we could still discover an imprint in the CMB, even while no pair of circles, much less ghost galaxy images, would remain. The topology of the universe could therefore provide information on what happens outside of the cosmological horizon [35].

Whatever the observational constraints, a lot of unsolved theoretical questions remain. The most fundamental one is the expected link between the present-day topology of space and its quantum origin, since classical general relativity does not allow for topological changes during the course of cosmic evolution. Theories of quantum gravity should allow us to address the problem of a quantum origin of space topology. For instance, in quantum cosmology, the question of the topology of the universe is completely natural. Quantum cosmologists seek to understand the quantum mechanism whereby our universe (as well as other ones in the framework of multiverse theories) came into being, endowed with a given geometrical and topological structure. We do not yet have a correct quantum theory of gravity, but there is no sign that such a theory would a priori demand that the universe have a trivial topology. Wheeler first suggested that the topology of space-­time might fluctuate at a quantum level, leading to the notion of a space-­time foam [36]. Additionally, some simplified solutions of the Wheeler-­‐‑de Witt equations for quantum cosmology show that the sum over all topologies involved in the calculation of the wavefunction of the universe is dominated by spaces with small volumes and multi-­connected topologies [37]. In the approach of brane worlds in string/M-­theories, the extra-­dimensions are often assumed to form a compact Calabi-­Yau manifold; in such a case, it would be strange that only the ordinary, large dimensions of our 3-­brane would not be compact like the extra ones. However, still at an early stage of development, string quantum cosmology can only provide heuristic indications on the way multi-­connected spaces would be favored.



Key People:

  • Jeffrey Weeks
  • Jean-Pierre Luminet
  • Neil Cornish


Key Sources of Research:


The Poincaré Dodecahedral Space and the Mystery of the Missing Fluctuations

Jeffrey Weeks


Click to access fea-weeks.pdf


Dodecahedral space topology as anexplanation for weak wide-angletemperature correlations in thecosmic microwave background

Jean-Pierre Luminet, Jeffrey R. Weeks, Alain Riazuelo ,Roland Lehoucq & Jean-Philippe Uzan

Click to access luminet-nat.pdf


A cosmic hall of mirrors


Jean-Pierre Luminet

Click to access 0509171.pdf



The Shape and Topology of the Universe

Jean-Pierre Luminet



Click to access 0802.2236.pdf


Luminet, Jean-Pierre.

The wraparound universe.

CRC Press, 2008.


Cosmic Topology : Twenty Years After

Jean-Pierre Luminet



Click to access 1310.1245.pdf


The Shape of Space after WMAP data

Jean-Pierre Luminet


Click to access v36_107.pdf



The Status of Cosmic Topology after Planck Data

Jean-Pierre Luminet

Click to access 1601.03884v2.pdf



Geometry and Topology in Relativistic Cosmology

Jean-Pierre Luminet


Click to access 0704.3374.pdf



Constraints on the Topology of the Universe: Extension to General Geometries

Pascal M. Vaudrevange,  Glenn D. Starkman, Neil J. Cornish, and David N. Spergel


Click to access 1206.2939.pdf



Topology of compact space forms from Platonic solids. I.

A. Cavicchioli∗, F. Spaggiari, A.I. Telloni


Topology of compact space forms from Platonic solids. II

A. Cavicchioli∗, F. Spaggiari, A.I. Telloni


Ancient Map of Universe and Modern Science

Jeoraj Jain


Discovering the Total Contents of the Universe

Jeoraj Jain


Poundstone, William.

The recursive universe: cosmic complexity and the limits of scientific knowledge.

Courier Corporation, 2013.

Author: Mayank Chaturvedi

You can contact me using this email mchatur at the rate of AOL.COM. My professional profile is on

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