Constraining slow-roll inflation in the presence of dynamical dark energy

In this Letter 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 {ϵi}. With the first order approximation in the slow-roll expansion, we find that the constraints on the horizon-flow parameters are ϵ1<0.014(95%C.L.) and ϵ2=0.034±0.024(1σ) in the ΛCDM model. In the framework of dynamical dark energy models, the constraints become obviously weak, ϵ1<0.022(95% C.L.) and ϵ2=−0.006±0.039(1σ), and the inflation models with a “blue” tilt, which are excluded about 2σ in the ΛCDM 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 ϵ3, the large running of the scalar spectral index is found for the ΛCDM model, as well as the dynamical dark energy models.