Single-field inflation constraints from CMB and SDSS data - Finelli, Fabio; Hamann, Jan; Leach, Samuel M; Lesgourgues, Julien (Journal of cosmology and astroparticle physics, 2010)
We present constraints on canonical single-field inflation derived from WMAP five year, ACBAR, QUAD, BICEP data combined with the halo power spectrum from SDSS LRG7. Models with a non-scale-invariant spectrum and a red tilt nsub S < 1 are now preferred over the Harrison-Zel'dovich model (nsub S = 1, tensor-to-scalar ratio r = 0) at high significance. Assuming no running of the spectral indices, we derive constraints on the parameters (nsub S, r) and compare our results with the predictions of simple inflationary models. The marginalised credible intervals read nsub S = 0.962{sup +0.028}{sub −0.026} and r < 0.17 (95% confidence level). With respect to previous analyses, the portion of the 68% c.l. contours compatible with potentials which are concave in the observable region becomes even smaller, but the quadratic potential model remains inside the 95% c.l. contours. We demonstrate that these results are robust to changes in the datasets considered and in the theoretical assumptions made. We then consider a non-vanishing running of the spectral indices by employing different methods, non-parametric but approximate, or parametric but exact. With our combination of CMB and LSS data, running models are preferred over power-law models only by a Δχ{sup 2} ≅ 5.8, allowing inflationary stages producing a sizable negative running −0.063{sup +0.061}{sub −0.049} and larger tensor-scalar ratio r < 0.33 at the 95% c.l. This requires large values of the third derivative of the inflaton potential within the observable range. We derive bounds on this derivative under the assumption that the inflaton potential can be approximated as a third order polynomial within the observable range.