WMAP Three Year Constraints on the Inflationary Expansion

We present the constraints on inflationary parameters in a flat $\Lambda$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). We discuss 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. 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 show that only when the third HFF $\epsilon_3 \ne 0$ is allowed with a very weak prior, an large negative (at $2 \sigma$) value for the running of the spectral index in standard inflation is found in any set of data we consider, i.e. CMB alone or CMB combined with LSS data sets.