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Abstract:

After a decade which has spawned an ever-enlarging zoo of inflationary models (see [1] for a recent review), we are now entering an era where observational advances will be sufficiently rapid as to impose significant constraints, with the possibility that inflationary models may be excluded more quickly than new ones devised. The most important constraints on inflationary models arise from the perturbation spectra which they produce, both density perturbations and gravitational waves. At this meeting much has been said about the gravitational waves, and rather less about the density perturbations. However, the present situation is that a variety of observations constrain the form of density perturbations whilst no positive detection has been made of gravitational waves, so at present one must concentrate on the former. It is well established that even if one allows the inflationary potential V (OE) for the inflaton field OE to be an arbitrary function, then barring pathologies the inflationary prediction is accurately given via the slow-roll approximation and depends only on two parameters [2, 3], the so-called slow-roll parameters ffl = m

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