  By making use of the background field method, the one-loop quantization for
Euclidean Einstein-Weyl quadratic gravity model on the de Sitter universe is
investigated. Using generalized zeta function regularization, the on-shell and
off-shell one-loop effective actions are explicitly obtained and one-loop
renormalizability, as well as the corresponding one-loop renormalization group
equations, are discussed. The so called critical gravity is also considered.
