Local gauge-invariant cosmological perturbations

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Abstract
We develop a gauge-invariant formalism suitable for the study of cosmological perturbations induced by defects. It consists in remolding the well-known Bardeen formalism into a local and gauge-invariant theory formulated in configuration space. Baradeen’s variables are first combined into local and gauge-invariant variables with simple geometric interpretations, and a system of hyperbolic equations is then derived for the new variables. The resulting theory is manifestly causal and it contains the density-gradient–vorticity interaction effect first discovered by Ellis, Bruni, and Hwang. Some applications to the theory of topological defects are given. The inborn metric of cosmic strings and the ‘‘stiff defect’’ approximation are reanalyzed, and a general solution for the density fluctuations induced by defects is given in terms of Green’s functions.