Painless causality in defect calculations

Abstract

Topological defects must respect causality, a statement leading to restrictive constraints on the power spectrum of the total cosmological perturbations they induce. Causality constraints have long been known to require the presence of an underdensity in the surrounding matter compensating the defect network on large scales. This so-called compensation can never be neglected and significantly complicates calculations in defect scenarios, e.g., computing cosmic microwave background fluctuations. A quick and dirty way to implement the compensation is the so-called compensation fudge factors. Here we derive the complete photon-baryon-CDM back reaction effects in defect scenarios. The fudge factor comes out as an algebraic identity and so we drop the negative qualifier ``fudge.'' The compensation scale is computed and physically interpreted. Secondary back reaction effects exist, and neglecting them constitutes the well-defined approximation scheme within which one should consider compensation factor calculations. We quantitatively assess the accuracy of this approximation, and conclude that the considerable pains associated with improving on it are often a waste of effort.