Scalar, vector, and tensor contributions to CMB anisotropies from cosmic defects

Recent work has emphasised the importance of vector and tensor contributions to the large scale microwave anisotropy fluctuations produced by cosmic defects. In this paper we provide a general discussion of these contributions, and how their magnitude is constrained by the fundamental assumptions of causality, scaling, and statistical isotropy. We discuss an analytic model which illustrates and explains how the ratios of isotropic and anisotropic scalar, vector and tensor stress-energy sources are determined. This provides a check of the results from large scale numerical simulations, confirming the numerical finding that vector and tensor modes provide substantial contributions to the large angle anisotropies. We show that the qualitative features of the stress-energy tensor carry over to the microwave background anisotropies. This leads to a suppression of the scalar normalization and consequently of the Doppler peaks.