Primordial fluctuations and cosmological inflation after WMAP 1.0

The observational constraints on the primordial power spectrum have tightened considerably with the release of the first year analysis of the WMAP observations, especially when combined with the results from other CMB experiments and galaxy redshift surveys. These observations allow us to constrain the physics of cosmological inflation: (i) The data show that the Hubble distance is almost constant during inflation. While observable modes cross the Hubble scale, it changes by less than 3% during one e-folding: d(d_H)/dt < 0.032 at 2 sigma. The distance scale of inflation itself remains poorly constrained: 1.2 x 10^{-28} cm < d_H < 1 cm. (ii) We present a new classification of single-field inflationary scenarios (including scenarios beyond slow-roll inflation), based on physical criteria, namely the behaviour of the kinetic and total energy densities of the inflaton field. The current data show no preference for any of the scenarios. (iii) For the first time the slow-roll assumption could be dropped from the data analysis and replaced by the more general assumption that the Hubble scale is (almost) constant during the observable part of inflation. We present simple analytic expressions for the scalar and tensor power spectra for this very general class of inflation models and test their accuracy.