Weyl tensor and gravitational entropy

There is a conjecture due to Penrose that there may be a relation between the Weyl curvature tensor and gravitational entropy. In this paper, this conjecture is studied in the context of a specific model, the Gowdy cosmology. The square of the curvature is calculated as an operator and its expectation values in states of clumped and unclumped gravitons are calculated. The results indicate that the curvature contains information about the entropy of the gravitational field.