ar X iv : a st ro - p h / 98 04 31 6 v 1 2 9 A pr 1 99 8 GIC Approach to Cosmic Background Radiation Anisotropies : Part 1 Tim Gebbie

This is the first of a series of papers extending a Gauge Invariant and Covariant (GIC) treatment of kinetic theory in curved space-times to a treatment of Cosmic Background Radiation (CBR) temperature anisotropies arising from inhomogeneities in the early universe. This paper deals with algebraic issues, both generically and in the context of models linearised about Robertson-Walker geometries . The approach represents radiation anisotropies by Projected Symmetric and Trace-Free tensors. The Angular correlation functions for the mode coefficients are found in terms of these quantities, following the Wilson-Silk approach, but derived and dealt with in GIC form. The covariant multipole and mode-expanded angular correlation functions are related to the usual treatments in the literature. The GIC mode expansion is related to the coordinate approach by linking the Legendre functions to the Projected Symmetric Trace-free representation, using a covariant addition theorem for the tensors to generate the Legendre Polynomial recursion relation. This paper lays the foundation for further papers in the series, which use this formalism in a GIC approach to develop solutions of the Boltzmann and Liouville equations for the CBR before and after decoupling, thus providing a unified GIC derivation of the variety of approaches to CBR anisotropies in the current literature.