3.3. Models of inflation

At present, understanding of fundamental physics is insufficient to give clear guidance as to how to build inflationary models. The present approach is therefore more phenomenological; we construct models of inflation, develop their predictions, and ultimately compare to observations in order to determine which properties are associated with successful models. So far, this approach has narrowed the range of possible models only modestly, and indeed theoretical ingenuity is creating new models more rapidly than observational improvements are ruling models out. Fortunately, it is projected that this state of affairs will soon change; upcoming observations of microwave anisotropies should have the capacity to exclude either all or nearly all of existing inflationary models.

A model of inflation consists of some number of scalar fields, plus a form for the potential of those fields. ⁽²⁾ It may also require a specification of the means for ending inflation. Ordinarily, the working assumption is that only a single scalar field is dynamically important during inflation, possibly with a second static field providing an additional contribution to the energy density (see the later discussion of hybrid inflation). This single-field paradigm is the simplest assumption that can be made, and a useful initial goal is to investigate how well such a model can be constrained by data, and indeed whether or not the entire class of single-field models can be excluded. In the latter eventuality, the question will arise as to whether a more complicated inflationary model can keep the theory alive, or if one has to abandon the inflationary model for structure formation altogether. I will say a little on this later, but for the most part this article restricts its attention to the single-field case.

Assuming that a single field gives the complete dynamics, the model is given by a choice of V(). Until recently, this potential would have been required to vanish at the minimum, in order not to generate an unfeasibly large cosmological constant today (we see from the effective density and pressure of a scalar field that a non-vanishing potential at the minimum gives the equation of state p = - mimicking a cosmological constant). In such a case, inflation will necessarily terminate as the field approaches the minimum. However, this assumption need not be made if a second static field supplies a contribution to the energy density, which may mean that the global potential minimum occurs for a value of this field differing from the one it has during inflation. It may therefore be necessary to specify the value _end at which inflation terminates, as well as the potential.

² It may also include such complexities as deviations from general relativity (for example as in scalar-tensor theories or the currently-popular braneworld scenario), extra dimensional physics, etc, which I will not explore here. Back.