The Weyl Curvature Conjecture

In this paper we review Penrose’s Weyl curvature conjecture which states that the concept of gravitational entropy and the Weyl tensor is somehow linked, at least in a cosmological setting. We give a description of a certain entity constructed from the Weyl tensor, from the very early history of our universe until the present day. Inflation is an important mechanism in our early universe for homogenisation and isotropisation, and thus it must cause large effects upon the evolution of the gravitational entropy. Therefore the effects from inflationary fluids and a cosmological constant are studied in detail. 1 The arrow of time and gravitational entropy in the context of a cosmology There is a strange omission in the traditional version of the second law of thermodynamics (SLT). It does not take gravity into account. However the existence of the arrow of time is usually explained with reference to SLT. And most discussions of the origin of the arrow of time appeal ultimately to the initial condition and the evolution of the universe. Gravity plays an essential role for this evolution. As pointed out by P.C.W. Davies [1, 2] there seems to be a paradox that the material contents of the universe began in a condition of thermodynamic equilibrium, whereas the universe today is far from equilibrium. Hence the thermodynamic entropy has been reduced in conflict with SLT which says that [email protected] [email protected]