We use Bardeen’s gauge-invariant formalism to analyze the behavior of, and relationship between, various geometric and physical quantities of cosmological interest at the linear level. This leads to a cosmologically oriented gauge-invariant characterization of the different perturbation modes that can arise. In particular a link is made between the existence of gravitational-wave modes and the conformal curvature of hypersurfaces in spacetime. We indicate how these results can be useful in the analysis of exact solutions of the Einstein field equations.

• Received 7 February 1989

DOI:https://doi.org/10.1103/PhysRevD.39.2882