Gravitational entropy and quantum cosmology

Abstract

We investigate the evolution of different measures of `gravitationalentropy'in Bianchi type I and Lemaître-Tolman universe models.A new quantity behaving in accordance with the second law ofthermodynamics is introduced. We then go on and investigate whether aquantum calculation of initial conditions for the universe based upon theWheeler-DeWitt equation supports Penrose's Weyl curvatureconjecture, according to which the Ricci part of the curvature dominatesover the Weyl part at the initial singularity of the universe. The theory isapplied to the Bianchi type I universe models with dust and acosmological constant and to the Lemaître-Tolman universe models. Weinvestigate two different versions of the conjecture. First, we investigatea local version which fails to support the conjecture. Thereafter weconstruct a non-local entity which shows more promising behaviourconcerning the conjecture.