Constraints on the inflationary expansion from three-year WMAP, small scale CMBanisotropies and large scale structure data sets

Abstract

We present the constraints on inflationary parameters in a flatΛCDM universe obtained from the Wilkinson Microwave Anisotropy Probe (WMAP)three-year data release, plus smaller scale cosmic microwave background (CMB)and two large scale structure (LSS) data sets, 2dF and the Sloan Digital SkySurvey (SDSS) (treated separately). We use a Markov chain Monte Carlo (MCMC)technique combined with an analytic description of the inflationary spectra in termsof the horizon flow functions (HFF). By imposing a consistency condition forthe tensor-to-scalar ratio, we study the constraints on both single field standardinflation and on inflation with the violation of the null energy condition, whichleads to a blue spectrum for gravitational waves. For standard inflation, theconstraint on the tensor-to-scalar ratio we obtain from CMB data and 2dF05 isr0.01<0.26 at2σ confidence level. Without the consistency condition between the tensor-to-scalar ratio and thetensor slope, the constraint on the tensor amplitude is not significantly changed, but theconstraints on the HFFs are significantly relaxed. We then show that when the third HFFϵ3 is allowed to be non-zero and to be of order unity, a large negative (at2σ) value for the running of the scalar spectral index in standard inflation is found in any setof data we consider.