What is the future of causal models of cosmic structure formation ? ∗ Andreas Albrecht

Recent research has severely constrained the standard “defect” models of cosmic structure formation. Here I discuss the nature of the problems with defect models, and place this discussion in the context of the big picture of cosmic structure formation. In particular, I classify models of cosmic structure formation as either “causal” or “acausal”, and ask whether the problems with the defect models extend to all other causal models. I argue that determining the causal nature of the primordial perturbations is within the reach of modern cosmology, and that such a determination would yield deep insights into the very early Universe. 1 Causality and cosmic structure There is now overwhelming evidence that the Universe is extremely homogeneous on large scales. This fact, combined with the tendency for gravity to make matter more clumpy as time goes on means that the early Universe was very smooth indeed. Still, the early Universe must have had some very small primordial inhomogeneities in order to seed the process of gravitational collapse and produce the observed structure in the Universe. Because ∗ To appear in the proceedings of the International Workshop on Particle Physics and the Early Universe Ambleside, September 1997, L. Roszkowski Ed. of the small amplitude required of these initial inhomogeneities, it has become common in cosmology to speak of the almost perfect homogeneity and the primordial perturbations as two separate features of the early Universe. The popular “inflationary cosmology” offers one explanation for the origin of both these features. During a period of cosmic inflation whatever initial homogeneities are present are pushed to such large scales that they are unobservable. The fluctuations on observable scales are predicted based on well-defined calculable processes which take zero-point quantum fluctuations in the quantum fields and amplify them into what ultimately become large scale classical perturbations in the cosmic matter. If the amplitude of these perturbations is tuned to be sufficiently small, the inflationary models predict that the “Standard Big Bang” (SBB) epoch which follows inflation will start out with the required homogeneity and primordial perturbations. Another popular paradigm, typified by the cosmic defect models, starts with a perfectly homogeneous universe which is already experiencing SBB evolution. At some point, physical processes (such as a phase transition) then produce inhomogeneities which can seed cosmic structure. The origin of the initial perfect homogeneity might still be inflation (for example some speculate that the fine tuning problem of the inflationary perturbation amplitude might actually be solved in nature by producing an absolutely infinitesimal perturbation amplitude[1, 2], resulting in an essentially perfectly homogeneous start to the SBB). Because this paradigm operates entirely within the SBB, the causality structure of the SBB is respected. In particular, matter cannot be moved around outside the causal horizon, and this severely constrains the nature of the perturbations on large scales. By contrast, the inflationary models have a very different causality structure, which allows in principle for arbitrary adiabatic perturbations to be produced on all relevant scales by the time the SBB epoch begins. Models such as inflation, for which outside-horizon perturbations are present at the start of the SBB are called, by convention, “acausal” models. Models which start with a homogeneous SBB and produce the perturbations in accordance with SBB causality are called “causal” models. Causal and acausal models of cosmic structure offer strikingly contrasting pictures, and it is thus of quite general interest to attempt to completely rule out one or the other on the basis of observations. In this article I pursue this goal by investigating the extent to which the known problems with the defect models reflect more general problems with other causal models. In