In Section 25.2 we considered the standard paradigm, according to which the curvature perturbation is generated by the vacuum fluctuation of the inflaton field during slow-roll inflation. We saw that observation gives considerable information about the potential when the pivot scale leaves the horizon. The normalization of the spectrum requires (V/∈)1/4 = 6.6 × 1016 GeV and the spectral index determines 2η − 6∈. Also, the bound on the running n′ constrains ξ, while the upper bound on the tensor fraction r constrains V.

If instead the curvature perturbation is generated after inflation, there is no particular reason to consider slow-roll inflation. If one does consider it, the only constraints are ∈ « 1 and (V/∈)1/4 « 6.6 × 1016 GeV (implying a small and probably negligible tensor fraction). In this chapter, we assume the standard paradigm and see how different models of slow-roll inflation are then constrained by observation.

By a model of inflation, we mean an effective field theory that is supposed to apply during inflation. In the end, it should be part of an effective field theory that takes us all the way from inflation to the present. A lot of work has been done in this direction, but so far no preferred model has emerged.

As we write, the Large Hadron Collider (LHC) is beginning operation, and may or may not find evidence for supersymmetry.