Weyl curvature hypothesis

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The Weyl curvature hypothesis (named after Hermann Weyl ), which appears in the context of the application of Albert Einstein's general theory of relativity to cosmology , was proposed in 1979 by the British mathematician and theoretical physicist Sir Roger Penrose in an article which provided explanations for two fundamental problems in the physics tries to enter. On the one hand, one would like to understand why our universe appears remarkably spatially homogeneous and isotropic on the largest accessible observation scales (and thus can be described mathematically by a simple Friedmann-Lemaître model ), on the other hand, this should address the fundamental question of the origin of the Second Law of the Thermodynamics are addressed.

In Penrose's view, an answer to these questions is deeply related to the concept of an entropy content of gravitational fields . Near the cosmological initial singularity (the Big Bang ), he suggests, the entropy content of the cosmological gravitational field is said to have been extremely low (compared to values ​​that would theoretically have been possible) and then began to increase monotonically. This process was expressed, for example, in the formation of structures by the clumping of matter, with the formation of galaxies and galaxy clusters . Penrose combines the initially very low entropy content of the universe with an effective disappearance of the Weyl curvature tensor of the cosmological gravitational field near the Big Bang. After that, he suspects, the dynamic influence of the Weyl curvature increased steadily, which is why it is responsible for a global increase in the amount of entropy in the universe. As a consequence, a cosmological arrow of time is induced.

The Weyl curvature represents gravitational effects such as tidal fields and gravitational radiation . Mathematically, Penrose's ideas on the Weyl curvature hypothesis were discussed in the context of so-called isotropic cosmological initial singularities. Penrose sees the Weyl curvature hypothesis as a physically more convincing alternative to cosmic inflation (a hypothetical phase of accelerated expansion of the young universe) in order to explain the almost complete spatial homogeneity and isotropy of the universe that can be observed today.

Individual evidence

  1. ^ R. Penrose: Singularities and Time-Asymmetry . In: SW Hawking, W. Israel (ed.): General Relativity: An Einstein Centenary Survey . Cambridge University Press, Cambridge 1979, pp. 581-638
  2. ^ SW Goode, J. Wainwright: Isotropic Singularities in Cosmological Models . In: Class. Quantum Grav. . 2, 1985, pp. 99-115. doi : 10.1088 / 0264-9381 / 2/1/010 .
  3. ↑ RPAC Newman: On the Structure of Conformal Singularities in Classical General Relativity . In: Proc. R. Soc. Lond. A . 443, 1993, pp. 473-492. doi : 10.1098 / rspa.1993.0158 .
  4. ↑ K. Anguige, KP Tod: Isotropic Cosmological Singularities I. Polytropic Perfect Fluid Spacetimes . In: Ann. Phys. NY . 276, 1999, pp. 257-293. doi : 10.1006 / aphy.1999.5946 .
  5. ^ WC Lim, H. van Elst, C. Uggla and J. Wainwright: Asymptotic Isotropization in Inhomogeneous Cosmology . In: Phys. Rev. D . 69, 2004, pp. 103507 (1-22). doi : 10.1103 / PhysRevD.69.103507 .
  6. ^ R. Penrose: Difficulties with Inflationary Cosmology . In: EJ Fergus (Ed.): Proc. 14 th Texas Symp. On Relativistic Astrophysics . NY Academy of Sciences, New York 1989, pp. 249-264, doi: 10.1111 / j.1749-6632.1989.tb50513.x