Gravitational entropy and the cosmological no-hair conjecture

The gravitational entropy and no-hair conjectures seem to predict contradictory future states of ourUniverse. The growth of the gravitational entropy is associated with the growth of inhomogeneity, while theno-hair conjecture argues that a universe dominated by dark energy should asymptotically approacha homogeneous and isotropic de Sitter state. The aim of this paper is to study these two conjectures. Theinvestigation is based on the Simsilun simulation, which simulates the universe using the approximation ofthe Silent Universe. The Silent Universe is a solution to the Einstein equations that assumes irrotational,nonviscous, and insulated dust, with vanishing magnetic part of the Weyl curvature. The initial conditionsfor the Simsilun simulation are sourced from the Millennium simulation, which results with a realisticallyappearing but relativistic at origin simulation of a universe. The Simsilun simulation is evolved from theearly universe (t = 25 Myr) until far future (t = 1000 Gyr). The results of this investigation show that bothconjectures are correct. On global scales, a universe with a positive cosmological constant and nonpositivespatial curvature does indeed approach the de Sitter state. At the same time it keeps generating thegravitational entropy