We consider small-field models which invoke the usual framework for the effective field theory, and large-field models which go beyond that. Present and future possibilities for discriminating between the models are assessed, on the assumption that the primordial curvature perturbation is generated during inflation. With PLANCK data, the theoretical and observational uncertainties on the spectral index will be comparable, providing useful discrimination between small-field models.Further discrimination between models may come later through the tensor fraction, the running of the spectral index and non-gaussianity. The prediction for the trispectrum in a generic multi-field inflation model is given for the first time.

Measuring the primordial power spectrum on small scales is a powerful tool in inflation model building, yet constraints from Cosmic Microwave Background measurements alone are insufficient to place bounds stringent enough to be appreciably effective. For the very small scale spectrum, those which subtend angles of less than 0.3 degrees on the sky, an upper bound can be extracted from the astrophysical constraints on the possible production of primordial black holes in the early universe. A recently discovered observational by-product of an enhanced power spectrum on small scales, induced gravitational waves, have been shown to be within the range of proposed space based gravitational wave detectors; such as NASA's LISA and BBO detectors, and the Japanese DECIGO detector. In this paper we explore the impact such a detection would have on models of inflation known to lead to an enhanced power spectrum on small scales, namely the Hilltop-type and running mass models. We find that the Hilltop-type model can produce observable induced gravitational waves within the range of BBO and DECIGO for integral and fractional powers of the potential within a reasonable number of e−folds. We also find that the running mass model can produce a spectrum within the range of these detectors, but require that inflation terminates after an unreasonably small number of e−folds. Finally, we argue that if the thermal history of the Universe were to accomodate such a small number of e−folds the Running Mass Model can produce Primordial Black Holes within a mass range compatible with Dark Matter, i.e. within a mass range 10 20 g M BH 10 27 g.

We consider a two-field hybrid inflation model, in which the curvature perturbation is predominantly generated at the end of inflation. By finely tuning the coupling of the fields to the waterfall we find that we can get a measurable amount of non-gaussianity.

We consider a two component hybrid inflation model, in which two fields drive inflation. Our results show that this model generates an observable non-gaussian contribution to the curvature spectrum, within the limits allowed by the recent WMAP year 3 data. We show that if one field has a mass η φ < 0, and an initial value φ < 0.06M pl while the other field has a mass ησ > 0, and initial field value 0.5M pl < σ ≤ M pl then the non-gaussianity is observable with 1 fNL < 1.5, but that fNL becomes much less than the observable limit should we take both masses to have the same sign, or if we loosened the constraints on the initial field values.

The survey of models in astro-ph/0510441 is updated. For the first time, a large fraction of the models is ruled out at more than 3σ.