Shape of the universe

Local and global geometry of the universe From Wikipedia, the free encyclopedia

Determination of the shape of the universe is a problem of physical cosmology.

Observational evidence (BOOMERANG Project, MAXIMA, Planck, WMAP) indicates that the observable universe is spatially flat.[1][2][3][4][5] It is unknown whether the universe is simply connected like euclidean space or multiply connected like a torus.[6]

The observable universe

See also: Distance measures (cosmology)

Human knowledge of the universe is restricted by the fact that any signal information from further than the cosmological horizon within the universe moving towards any position of human perception or telescope is non available. [7]

Possible shapes of the universe

Further information: Curvature § Space, and Flatness problem
The local geometry of the universe is determined by whether the density parameter Ω is greater than, less than, or equal to 1. From top to bottom: a spherical universe with Ω > 1, a hyperbolic universe with Ω < 1, and a flat universe with Ω = 1. These depictions of two-dimensional surfaces are merely easily visualizable analogs to the 3-dimensional structure of (local) space.

Einstein stated, by the law of gravitation, heavy masses curve space-time. [8] The curvature of spacetime is the same as the density parameter, [9] represented with Ω (omega). The density parameter is the average density of the universe divided by the critical energy density, that is, the mass energy needed for a universe to be flat. Put another way,

  • If Ω > 1, there is positive curvature.
  • If Ω < 1, there is negative curvature.
  • If Ω = 1, the universe is flat.

Scientists could experimentally calculate Ω to determine the curvature two ways. One is to count all the mass–energy in the universe and take its average density, then divide that average by the critical energy density. Data from the Wilkinson Microwave Anisotropy Probe (WMAP) as well as the Planck spacecraft give values for the three constituents of all the mass–energy in the universe – normal mass (baryonic matter and dark matter), relativistic particles (predominantly photons and neutrinos), and dark energy or the cosmological constant:[10][11]

Another way to measure Ω is to do so geometrically by measuring an angle across the observable universe. This can be done by using the CMB and measuring the power spectrum and temperature anisotropy. For instance, one can imagine finding a gas cloud that is not in thermal equilibrium due to being so large that light speed cannot propagate the thermal information. Knowing this propagation speed, we then know the size of the gas cloud as well as the distance to the gas cloud, we then have two sides of a triangle and can then determine the angles. Using a method similar to this, the BOOMERanG experiment has determined that the sum of the angles to 180° within experimental error, corresponding to Ωtotal ≈ 1.00±0.12.[12]

The Friedmann–Lemaître–Robertson–Walker (FLRW) model using Friedmann equations is commonly used to model the universe.

Global universal structure

As stated in the introduction, investigations within the study of the global structure of the universe include:

  • whether the universe is infinite or finite in extent,
  • whether the geometry of the global universe is flat, positively curved, or negatively curved
  • whether the topology is simply connected (for example, like a sphere) or else multiply connected (for example, like a torus).[13]

Infinite or finite

One of the unresolved questions about the universe is whether it is infinite or finite in extent.[14][15] Answers within the 21st century depend on the current standard cosmological model.[16]

Ancient mythologies variously described the universe as finite.[17]

By way of the account of Diogenes Laërtius, for Leucippus[18] (c. 5th century BC)[19] the universe is spatially infinite.[18] Eudoxus (c. 380 BC)[20][a] in thought of motion considered the stars integral to a sphere.[22][23][24] The concept of Aristotle[25][26] (384–322 BC),[27] concentric spheres[25][26] existed outgoing from Earth, the furthest contained the stars and was sometimes termed the kosmos,[26] outside of which there was nothing;[28][29][26] neither any place, time, or void extracosmic.[29][30]

From the concepts of Aristotle[31][32][b] which became the mode for Ptolemy[36][31] (2nd century AD[37] post[36] Ὑποθέσεις τῶν πλανωμένων[38]) the preferred[36] general cosmology[20] into the Middle Ages was the cosmos was finite[31] because of Aristotelian cosmology.[36] Dante Alighieri, Paradiso,[39] (1308–1320)[40] conceived of a Ptolemaic understanding universe which explained the Earth was central to spheres the outer of which was the realm of God, the perception of all prominent medieval era thinkers.[39] Bradwardine (1344) and Oresme during the 14th century contested the Aristotlian view on the basis of infinite God.[41]

The advent of the heliocentric model produced in scientific thought the possibility of an infinite universe.[42] A Universe infinite in size, using Copernicus, explained by Thomas Digges in: A perfit description of the caelestiall orbs, published 1576, was a conceptual break from the tradition of the reality of a celestial outer realm known as Paradise.[43]

Einstein in consideration of his general theory of relativity[44] (1916)[41] demonstrated in Kosmologische Betrachtungen zur allgemeinen Relativitätstheorie (1917) a finite universe.[44] The de Sitter infinite universe (1917) was caused by incompatibility of Relativity and Euclidean space.[41] Hilbert (1925) thought the universe was determined finite by elliptical geometry or infinite by Euclidean geometry[45] (i.e. flat).[46]

The factor which could determine from our position in the universe (and the 21st century) a scientific answer of which version of the universe is thought reality with regards to the geometry of the universe is: if positively curved is finite, if flat or negatively curved is infinite.[47] A finite universe is volumetrical,[48][46] an infinite universe could encompass an infinity of space with a finite amount of matter.[48]

Observational methods

In the 1990s and early 2000s, empirical methods for determining the global topology using measurements on scales that would show multiple imaging were proposed[49] and applied to cosmological observations.[50][51]

In the 2000s and 2010s, it was shown that, since the universe is inhomogeneous as shown in the cosmic web of large-scale structure, acceleration effects measured on local scales in the patterns of the movements of galaxies should, in principle, reveal the global topology of the universe.[52][53][54]

Curvature

The curvature of the universe places constraints on the topology. If the spatial geometry is spherical, i.e., possess positive curvature, the topology is compact. For a flat (zero curvature) or a hyperbolic (negative curvature) spatial geometry, the topology can be either compact or infinite.[49] Many textbooks erroneously state that a flat or hyperbolic universe implies an infinite universe; however, the correct statement is that a flat universe that is also simply connected implies an infinite universe.[49]

The latest research shows that even the most powerful future experiments (like the SKA) will not be able to distinguish between a flat, open and closed universe if the true value of cosmological curvature parameter is smaller than 10−4. If the true value of the cosmological curvature parameter is larger than 10−3 we will be able to distinguish between these three models even now.[55]

Final results of the Planck mission, released in 2018, show the cosmological curvature parameter, 1 − Ω = ΩK = −Kc2/a2H2, to be 0.0007±0.0019, consistent with a flat universe.[56]

Universe with zero curvature

A flat universe can have zero total energy.[57]

Universe with positive curvature

Poincaré dodecahedral space is a positively curved space, colloquially described as "soccerball-shaped", as it is the quotient of the 3-sphere by the binary icosahedral group, which is very close to icosahedral symmetry, the symmetry of a soccer ball. This was proposed by Jean-Pierre Luminet and colleagues in 2003[50][58] and an optimal orientation on the sky for the model was estimated in 2008.[51]

Universe with negative curvature

A hyperbolic universe, one of a negative spatial curvature, is described by hyperbolic geometry, and can be thought of locally as a three-dimensional analog of an infinitely extended saddle shape. There are a great variety of hyperbolic 3-manifolds, and their classification is not completely understood. Those of finite volume can be understood via the Mostow rigidity theorem. For hyperbolic local geometry, many of the possible three-dimensional spaces are informally called "horn topologies", so called because of the shape of the pseudosphere, a canonical model of hyperbolic geometry. An example is the Picard horn, a negatively curved space, colloquially described as "funnel-shaped".[59]

See also

Notes

  1. [a]
    ἐν τρισὶν ἐτίθετ᾽ εἶναι σφαίραις, ὧν τὴν μὲν πρώτην τὴν τῶν ἀπλανῶν ἄστρων εἶναι [21]
  2. [b]
    Aristotle knew of the thoughts of Leucippus (and Democritus)[33] and considered the possibility of an infinite universe.[34][35]

References

External links

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