Difficulties with inflationary cosmology

The problems posed for inflationary cosmological models by (1) the large-scale homogeneity of the universe and (2) the second law of thermodynamics are considered theoretically. The analyses of Penrose (1979, 1981, 1988, and 1989) are summarized and illustrated with graphs and diagrams. Particular attention is given to the definition of entropy in the cosmological context, gravitational entropy, the low entropy of the big bang, and the Weyl curvature hypothesis.