PAINLESS CAUSALITY IN DEFECT CALCULATIONS

Topological defects must respect causality, a statement leading to res trictive constraints on the power spectrum of the total cosmological p erturbations they induce. Causality constraints have long been known t o require the presence of an underdensity in the surrounding matter co mpensating the defect network on large scales. This so-called compensa tion can be neglected and significantly complicates calculations in de fect scenarios, e.g., computing cosmic microwave background fluctuatio ns. A quick adn dirty way to implement the compensation is the so-call ed compensation fudge factors. Here we derive the complete photon-bary on-CDM back reaction effects in defect scenarios. The fudge factor com es out as an algebraic identity and so we drop the negative qualifier ''fudge.'' The compensation scale is computed and physically interpret ed. Secondary back reaction effects exist, and neglecting them constit utes the well-defined approximation scheme within which one should con sider compensation factor calculations. We quantitatively assess the a ccuracy of this approximation, and conclude that the considerable pain s associated with improving on it are often a waste of effort.