Inflation after WMAP3: confronting the slow-roll and exact power spectra with CMB data

The implications of the WMAP (Wilkinson Microwave Anisotropy Probe) third year data for inflation are investigated using both the slow-roll approximation and an exact numerical integration of the inflationary power spectra including a phenomenological modelling of the reheating era. At slow-roll leading order, the constraints epsilon1 < 0.022 and −0.07 < epsilon2 < 0.07 are obtained at the 95% CL (confidence level) implying a tensor to scalar ratio r10 < 0.21 and a Hubble parameter during inflation H/mPl < 1.3 × 10−5. At next-to-leading order, a tendency for epsilon3 > 0 is observed. With regard to the exact numerical integration, large field models, V(\phi)\propto \phi^p , with p > 3.1 are now excluded at the 95% CL. Small field models, V(\phi)\propto 1-(\phi /\mu)^p , are still compatible with the data for all values of p. However, if μ/mPl < 10 is assumed, then the case p = 2 is slightly disfavoured. In addition, mild constraints on the reheating temperature for an extreme equation of state w_{\mathrm {reh}}\gtrsim-1/3 are found, namely Treh > 2 TeV at the 95% CL. Hybrid models are disfavoured by the data, the best fit model having \Delta \chi ^2\simeq+5 with two extra parameters in comparison with large field models. Running mass models remain compatible, but no prior independent constraints can be obtained. Finally, superimposed oscillations of trans-Planckian origin are studied. The vanilla slow-roll model is still the most probable one. However, the overall statistical weight in favour of superimposed oscillations has increased in comparison with the WMAP first year data, the amplitude of the oscillations satisfying 2|x|σ0 < 0.76 at the 95% CL. The best fit model leads to an improvement of \Delta \chi^2\simeq-12 for three extra parameters. Moreover, compared to other oscillatory patterns, the logarithmic shape is favoured.