Can Conformal Weyl Gravity be Considered a Viable Cosmological Theory?

We present exact analytical solutions to the Conformal Weyl Gravity cosmological equations that are valid for both the matter and radiation dominated eras. The Primordial Nucleosynthesis process is also exhaustively studied. The main conclusion of our work is that cosmological models derived from this theory are not likely to reproduce the observational properties of our Universe. They fail to fulfill simultaneously the observational constraints on present cosmological parameters and on primordial light element abundances.