  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.
