GAUGE-INVARIANCE AND THE COSMIC MICROWAVE BACKGROUND-RADIATION TEMPERATURE

In recent years the Sachs-Wolfe anisotropy of the cosmic microwave rad iation has been carefully calculated using gauge-invariant formalisms, like that of Bardeen (1980). We carefully reexamine the most detailed of these, that by Panek (1986), particularly the underlying gauge-inv ariance properties of the calculation, the gauge choice of the observe d background temperature, the definition of the last-scattering surfac e, and the key steps of the analysis. We also treat other somewhat neg lected aspects of the usual calculations-the directional differencing which is an important feature of the anisotropy observations, the limi tations of scalar-vector-tensor decomposition, and the compensation ef fect. Our work essentially confirms the result Panek gives in the adia batic case, but suggests certain improvements and corrections of subtl e details to the way the calculation is actually performed and interpr eted. We also extend the calculation to the nonadiabatic case in an ex plicitly gauge-invariant way.