Constraining Slow-Roll Inflation in the Presence of Dynamical Dark Energy

In this paper we perform a global analysis of the constraints on the inflationary parameters in the presence of dynamical dark energy models from the current observations, including the three-year Wilkinson Microwave Anisotropy Probe (WMAP3) data, Boomerang-2K2, CBI, VSA, ACBAR, SDSS LRG, 2dFGRS and ESSENCE (192 sample). We use the analytic description of the inflationary power spectra in terms of the Horizon-flow parameters $\{\epsilon_i\}$. With the first order approximation in the slow-roll expansion, we find that the constraints on the Horizon-flow parameters are $\epsilon_1<0.014 (95$ and $\epsilon_2=0.034\pm0.024 (1\sigma)$ in the $\Lambda$CDM model. In the framework of dynamical dark energy models, the constraints become obviously weak, $\epsilon_1<0.022 (95$ and $\epsilon_2=-0.006\pm0.039 (1\sigma)$, and the inflation models with a "blue" tilt, which are excluded about $2\sigma$ in the $\Lambda$CDM model, are allowed now. With the second order approximation, the constraints on the Horizon-flow parameters are significantly relaxed further. If considering the non-zero $\epsilon_3$, the large running of the scalar spectral index is found for the $\Lambda$CDM model, as well as the dynamical dark energy models.