INITIAL CONDITIONS FOR INFLATION

Inflation has attracted cosmologists because of its potential to free the standard big bang model from its worst flaw. the need for special initial conditions and, in particular, the requirement of initial acausal homogeneity. Naturally one must check whether inflation itself depends critically on initial conditions. Several "no hair" theorems and perturbation calculations have indicated that inflation is stable, and that it will take place when the initial conditions are perturbed. This has led to the belief that inflation will start in any generic universe. On the other hand, since most studies of inflation were carried out in a FRW background. inflation has been criticized and it was suggested that. like the big bang model, it depends heavily on an unnatural homogeneous initial state. Great progress has been achieved in the last few years in understanding which conditions are indeed necessary for inflation to begin. In this paper we review the various conditions required for the onset of both "chaotic" and "new" inflation. We review the various studies of the effects of the scalar field kinetic term, the cosmological "no hair" conjecture. the possible roles of curvature and anisotropy, and the influence of inhomogeneities. We describe the essential conditions for the onset of inflation for all these cases. We show that "chaotic" inflation is not very sensitive to the initial conditions. It requires that the average value of the scalar field be larger than a few m(pl) over a region of several initial horizon radii; short-wavelength gradients on top of a high average field will generally not prevent inflation. "New" inflation is much more dependent on the initial conditions and, unless the potential is extremely flat. it requires that after the "new" inflation phase transition the scalar field must be localized at rest on the top of its potential at the origin. While our main objective is to classify the different initial conditions required for inflation, we also discuss some of the physical significance of these conditions. For example, we address the issue of whether the conditions that we find necessary for "chaotic" inflation prevail in the post quantum era early universe. These prerequisites could have far-reaching implications for inflationary models and for quantum cosmology and particle physics.