Weyl curvature hypothesis

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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.

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[edit]


  1. ^ R. Penrose (1979). "Singularities and Time-Asymmetry". In S. W. Hawking; W. Israel. General Relativity: An Einstein Centenary Survey. Cambridge University Press. pp. 581–638. 
  2. ^ S. W. Goode & J. Wainwright (1985). "Isotropic Singularities in Cosmological Models". Class. Quantum Grav. 2 (1): 99–115. Bibcode:1985CQGra...2...99G. doi:10.1088/0264-9381/2/1/010. 
  3. ^ 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. Bibcode:1993RSPSA.443..473N. doi:10.1098/rspa.1993.0158. 
  4. ^ K. Anguige & K. P. Tod (1999). "Isotropic Cosmological Singularities I. Polytropic Perfect Fluid Spacetimes". Annals of Physics. 276 (2): 257–293. arXiv:gr-qc/9903008Freely accessible. Bibcode:1999AnPhy.276..257A. doi:10.1006/aphy.1999.5946. 
  5. ^ W. C. Lim; H. van Elst; C. Uggla & J. Wainwright (2004). "Asymptotic Isotropization in Inhomogeneous Cosmology". Phys. Rev. D. 69 (10): 103507 (1–22). arXiv:gr-qc/0306118Freely accessible. Bibcode:2004PhRvD..69j3507L. doi:10.1103/PhysRevD.69.103507. 
  6. ^ R. Penrose (1989). "Difficulties with Inflationary Cosmology". In E. J. Fergus. Proc. 14th Texas Symp. on Relativistic Astrophysics. New York Academy of Sciences. pp. 249–264. doi:10.1111/j.1749-6632.1989.tb50513.x.