Constraints on the Inflationary Expansion from Three Year WMAP, small scale CMB anisotropies and Large Scale Structure Data Sets

Abstract

We present the constraints on inflationary parameters in a flat $Λ$CDM universe obtained by WMAP three year data release, plus smaller scale CMB and two LSS data sets, 2dF and SDSS (treated separately). We use a Markov Chain Monte Carlo (MCMC) technique combined with an analytic description of the inflationary spectra in terms of the horizon flow functions (HFF). By imposing a consistency condition for the tensor-to-scalar ratio, we study the constraints both on single field standard inflation and on inflation with the violation of the null energy condition, which leads to a blue spectrum for gravitational waves. For standard inflation, the constraint on the tensor-to-scalar ratio we obtain from CMB data and 2dF05 is: $r_{0.01} < 0.26$ at 2 $σ$ cl. Without the consistency condition between the tensor-to-scalar ratio and the tensor slope, the constraints on the tensor amplitude is not significantly changed, but the constraints on the HFFs are significantly relaxed. We then show that when the third HFF $ε_3$ is allowed to be non-zero and to be of order unity, a large negative (at $2 σ$) value for the running of the scalar spectral index in standard inflation is found in any set of data we consider.