Causality and the Doppler peaks

A considerable experimental effort is underway to detect the ''Doppler peaks'' in the angular power spectrum of the cosmic microwave anisotropy. These peaks offer unique information about structure formation in the universe. One key issue is whether structure could have formed by the action of causal physics within the standard hot big bang, or whether a prior period of inflation was required. Recently there has been some discussion of whether causal sources could reproduce the pattern of Doppler peaks produced by the standard adiabatic theory. This paper gives a rigorous definition of causality, and a causal decomposition of a general source. I present an example of a very simple causal source that mimics the standard adiabatic theory, accurately reproducing the behavior of the local intrinsic temperature perturbations.