Primordial fluctuations and cosmological inflation after WMAP 1.0

Abstract

The observational constraints on the primordial power spectrum have tightenedconsiderably with the release of the first-year analysis of the WMAP observations,especially when combined with the results from other CMB experiments and galaxyred-shift surveys. These observations allow us to constrain the physics of cosmologicalinflation:(i) The data show that the Hubble distance is almost constant during inflation.While observable modes cross the Hubble scale, it changes by less than3% during one e-folding: at 2σ. The distance scale of inflation itself remains poorly constrained:1.2 × 10−28 cm<dH<1 cm.(ii) We present a new classification of single-field inflationary scenarios (including scenariosbeyond slow-roll inflation), based on physical criteria, namely the behaviour of the kineticand total energy densities of the inflaton field. The current data show no preference for anyof the scenarios.(iii) For the first time the slow-roll assumption could be dropped from the data analysis andreplaced by the more general assumption that the Hubble scale is (almost) constant duringthe observable part of inflation. We present simple analytic expressions for the scalar andtensor power spectra for this very general class of inflation models and test their accuracy.