  We investigate the evolution of cosmological perturbations during de Sitter
inflation in the Einstein-Chern-Simons-Weyl gravity. Primordial massive
gravitational waves are composed of one scalar, two vector and four tensor
circularly polarized modes. We show that the vector power spectrum decays
quickly like a transversely massive vector in the superhorizon limit $z\to 0$.
In this limit, the power spectrum coming from massive tensor modes decays
quickly, leading to the conventional tensor power spectrum. Also, we find that
in the limit of $m^2 \to 0$ (keeping the Weyl-squared term only), the vector
and tensor power spectra disappear. It implies that their power spectra are not
gravitationally produced because they (vector and tensor) are decoupled from
the expanding de Sitter background, as a result of conformal invariance.
