Weyl curvature hypothesis: Difference between revisions
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| ⚫ | {{dablink|This article concerns [[Roger Penrose]]'s 1979 '''Weyl curvature hypothesis''', which would justify spatial homogeneity and isotropy of the observable part of the Universe in the [[Big Bang]] model. A different article discusses [[Weyl's postulate]], which is an assumption relating to separation of space and time in the [[Big Bang]] model.}} |
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{{Expert-subject|Physics|date=November 2008}} |
{{Expert-subject|Physics|date=November 2008}} |
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| ⚫ | {{dablink|This article concerns [[Roger Penrose]]'s 1979 '''Weyl curvature hypothesis''', which would justify spatial homogeneity and isotropy of the observable part of the Universe in the [[Big Bang]] model. A different article discusses [[Weyl's postulate]], which is an assumption relating to separation of space and time in the [[Big Bang]] model.}} |
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The '''Weyl curvature hypothesis''', which arises in the application of [[Albert Einstein]]'s [[general theory of relativity]] to [[physical cosmology]], was introduced by the British mathematician and theoretical physicist [[Sir Roger Penrose]] in an article in 1979<ref>{{cite conference | author = R. Penrose | title = Singularities and Time-Asymmetry | booktitle = General Relativity: An Einstein Centenary Survey | editor = S. W. Hawking and W. Israel | publisher = Cambridge University Press | year = 1979 | pages = 581–638}}</ref> in an attempt to provide explanations for two of the most fundamental issues in physics. On the one hand one would like to account for a [[Universe]] which on its largest observational scales appears remarkably spatially homogeneous and isotropic in its physical properties (and so can be described by a simple [[Robertson-Walker coordinates|Friedmann-Lemaître model]]), on the other hand there is the deep question on the origin of the [[second law of thermodynamics]]. |
The '''Weyl curvature hypothesis''', which arises in the application of [[Albert Einstein]]'s [[general theory of relativity]] to [[physical cosmology]], was introduced by the British mathematician and theoretical physicist [[Sir Roger Penrose]] in an article in 1979<ref>{{cite conference | author = R. Penrose | title = Singularities and Time-Asymmetry | booktitle = General Relativity: An Einstein Centenary Survey | editor = S. W. Hawking and W. Israel | publisher = Cambridge University Press | year = 1979 | pages = 581–638}}</ref> in an attempt to provide explanations for two of the most fundamental issues in physics. On the one hand one would like to account for a [[Universe]] which on its largest observational scales appears remarkably spatially homogeneous and isotropic in its physical properties (and so can be described by a simple [[Robertson-Walker coordinates|Friedmann-Lemaître model]]), on the other hand there is the deep question on the origin of the [[second law of thermodynamics]]. |
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Penrose suggests that the resolution of both of these problems is rooted in a concept of the [[entropy]] content of [[gravitational field]]s. Near the [[gravitational singularity|initial cosmological singularity]] (the [[Big Bang]]), he proposes, the entropy content of the cosmological gravitational field was extremely low (compared to what it theoretically could have been), and started rising monotonically thereafter. This process manifested itself e.g. in the formation of structure through the clumping of matter to form [[galaxies]] and [[clusters of galaxies]]. Penrose associates the initial low entropy content of the Universe with the effective vanishing of the [[Weyl curvature]] [[tensor]] of the cosmological gravitational field near the Big Bang. From then on, he proposes, its dynamical influence gradually increased, thus being responsible for an overall increase in the amount of entropy in the Universe, and so inducing a cosmological [[arrow of time]]. |
Penrose suggests that the resolution of both of these problems is rooted in a concept of the [[entropy]] content of [[gravitational field]]s. Near the [[gravitational singularity|initial cosmological singularity]] (the [[Big Bang]]), he proposes, the entropy content of the cosmological gravitational field was extremely low (compared to what it theoretically could have been), and started rising monotonically thereafter. This process manifested itself e.g. in the formation of structure through the clumping of matter to form [[galaxies]] and [[clusters of galaxies]]. Penrose associates the initial low entropy content of the Universe with the effective vanishing of the [[Weyl curvature]] [[tensor]] of the cosmological gravitational field near the Big Bang. From then on, he proposes, its dynamical influence gradually increased, thus being responsible for an overall increase in the amount of entropy in the Universe, and so inducing a cosmological [[arrow of time]]. |
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The Weyl curvature represents such gravitational effects as [[tidal force|tidal fields]] and [[gravitational radiation]]. Mathematical treatments of Penrose's ideas on the Weyl curvature hypothesis have been given in the context of isotropic initial cosmological singularities e.g. in the articles.<ref>{{cite journal | author=S. W. Goode and J. Wainwright | title=Isotropic Singularities in Cosmological Models | journal=Class. Quantum Grav. | volume=2 | year=1985 | issue=1 | pages=99–115 | doi=10.1088/0264-9381/2/1/010}}</ref><ref>{{cite journal | author=R. P. A. C. Newman | title=On the Structure of Conformal Singularities in Classical General Relativity | journal=Proc. R. Soc. Lond. A | volume=443 | year=1993 | issue=1919 | pages=473–492 | doi=10.1098/rspa.1993.0158}}</ref><ref>{{cite journal | author=K. Anguige and K. P. Tod | title=Isotropic Cosmological Singularities I. Polytropic Perfect Fluid Spacetimes | journal=Ann. Phys. N.Y. | volume=276 | issue=2 | year=1999 | pages=257–293 | doi=10.1006/aphy.1999.5946 | |
The Weyl curvature represents such gravitational effects as [[tidal force|tidal fields]] and [[gravitational radiation]]. Mathematical treatments of Penrose's ideas on the Weyl curvature hypothesis have been given in the context of isotropic initial cosmological singularities e.g. in the articles.<ref>{{cite journal | author=S. W. Goode and J. Wainwright | title=Isotropic Singularities in Cosmological Models | journal=Class. Quantum Grav. | volume=2 | year=1985 | issue=1 | pages=99–115 | doi=10.1088/0264-9381/2/1/010}}</ref><ref>{{cite journal | author=R. P. A. C. Newman | title=On the Structure of Conformal Singularities in Classical General Relativity | journal=Proc. R. Soc. Lond. A | volume=443 | year=1993 | issue=1919 | pages=473–492 | doi=10.1098/rspa.1993.0158}}</ref><ref>{{cite journal | author=K. Anguige and K. P. Tod | title=Isotropic Cosmological Singularities I. Polytropic Perfect Fluid Spacetimes | journal=Ann. Phys. N.Y. | volume=276 | issue=2 | year=1999 | pages=257–293 | doi=10.1006/aphy.1999.5946 | arxiv=gr-qc/9903008 }}</ref><ref>{{cite journal | author=W. C. Lim, H. van Elst, C. Uggla and J. Wainwright| title=Asymptotic Isotropization in Inhomogeneous Cosmology | journal=Phys. Rev. D | volume=69 | issue=10 | year=2004 | pages=103507 (1–22) | doi=10.1103/PhysRevD.69.103507 | arxiv=gr-qc/0306118 }}</ref> Penrose views the Weyl curvature hypothesis as a physically more credible alternative to [[cosmic inflation]] (a hypothetical phase of accelerated expansion in the early life of the Universe) in order to account for the presently observed almost spatial homogeneity and isotropy of our Universe.<ref>{{cite conference | author = R. Penrose | title = Difficulties with Inflationary Cosmology | booktitle = Proc. 14th Texas Symp. on Relativistic Astrophysics | editor = E. J. Fergus | publisher = New York Academy of Sciences | year = 1989 | pages = 249–264 | doi = 10.1111/j.1749-6632.1989.tb50513.x}}</ref> |
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==See also== |
==See also== |
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*[[Gravitational entropy]] |
*[[Gravitational entropy]] |
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Revision as of 05:51, 13 September 2011
 | This article needs attention from an expert in Physics. Please add a reason or a talk parameter to this template to explain the issue with the article. (November 2008) |
The Weyl curvature hypothesis, which arises in the application of Albert Einstein's general theory of relativity to physical cosmology, was introduced by the British mathematician and theoretical physicist Sir Roger Penrose in an article in 1979[1] in an attempt to provide explanations for two of the most fundamental issues in physics. On the one hand one would like to account for a Universe which on its largest observational scales appears remarkably spatially homogeneous and isotropic in its physical properties (and so can be described by a simple Friedmann-Lemaître model), on the other hand there is the deep question on the origin of the second law of thermodynamics.
Penrose suggests that the resolution of both of these problems is rooted in a concept of the entropy content of gravitational fields. Near the initial cosmological singularity (the Big Bang), he proposes, the entropy content of the cosmological gravitational field was extremely low (compared to what it theoretically could have been), and started rising monotonically thereafter. This process manifested itself e.g. in the formation of structure through the clumping of matter to form galaxies and clusters of galaxies. Penrose associates the initial low entropy content of the Universe with the effective vanishing of the Weyl curvature tensor of the cosmological gravitational field near the Big Bang. From then on, he proposes, its dynamical influence gradually increased, thus being responsible for an overall increase in the amount of entropy in the Universe, and so inducing a cosmological arrow of time.
The Weyl curvature represents such gravitational effects as tidal fields and gravitational radiation. Mathematical treatments of Penrose's ideas on the Weyl curvature hypothesis have been given in the context of isotropic initial cosmological singularities e.g. in the articles.[2][3][4][5] Penrose views the Weyl curvature hypothesis as a physically more credible alternative to cosmic inflation (a hypothetical phase of accelerated expansion in the early life of the Universe) in order to account for the presently observed almost spatial homogeneity and isotropy of our Universe.[6]
See also
References
- ^ R. Penrose (1979). "Singularities and Time-Asymmetry". In S. W. Hawking and W. Israel (ed.). General Relativity: An Einstein Centenary Survey. Cambridge University Press. pp. 581–638.
{{cite conference}}: Unknown parameter|booktitle=ignored (|book-title=suggested) (help) - ^ S. W. Goode and J. Wainwright (1985). "Isotropic Singularities in Cosmological Models". Class. Quantum Grav. 2 (1): 99–115. doi:10.1088/0264-9381/2/1/010.
- ^ R. P. A. C. Newman (1993). "On the Structure of Conformal Singularities in Classical General Relativity". Proc. R. Soc. Lond. A. 443 (1919): 473–492. doi:10.1098/rspa.1993.0158.
- ^ K. Anguige and K. P. Tod (1999). "Isotropic Cosmological Singularities I. Polytropic Perfect Fluid Spacetimes". Ann. Phys. N.Y. 276 (2): 257–293. arXiv:gr-qc/9903008. doi:10.1006/aphy.1999.5946.
- ^ W. C. Lim, H. van Elst, C. Uggla and J. Wainwright (2004). "Asymptotic Isotropization in Inhomogeneous Cosmology". Phys. Rev. D. 69 (10): 103507 (1–22). arXiv:gr-qc/0306118. doi:10.1103/PhysRevD.69.103507.
{{cite journal}}: CS1 maint: multiple names: authors list (link) - ^ R. Penrose (1989). "Difficulties with Inflationary Cosmology". In E. J. Fergus (ed.). Proc. 14th Texas Symp. on Relativistic Astrophysics. New York Academy of Sciences. pp. 249–264. doi:10.1111/j.1749-6632.1989.tb50513.x.
{{cite conference}}: Unknown parameter|booktitle=ignored (|book-title=suggested) (help)