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 \epsilon _ { 1 } < 0.022 and -0.07 < \epsilon _ { 2 } < 0.07 are obtained at 95 \% CL ( Confidence Level ) implying a tensor-to-scalar ratio r _ { 10 } < 0.21 and a Hubble parameter during inflation H / m _ { \scriptscriptstyle { \mathrm { Pl } } } < 1.3 \times 10 ^ { -5 } .
At next-to-leading order , a tendency for \epsilon _ { 3 } > 0 is observed .
With regards to the exact numerical integration , large field models , V ( \phi ) \propto \phi ^ { p } , with p > 3.1 are now excluded at 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 \mu / m _ { \scriptscriptstyle { \mathrm { Pl } } } < 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 T _ { \mathrm { reh } } > 2 \mbox { TeV } at 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| \sigma _ { 0 } < 0.76 at 95 \% CL .
The best fit model leads to an improvement of \Delta \chi ^ { 2 } \simeq - 12 for 3 extra parameters .
Moreover , compared to other oscillatory patterns , the logarithmic shape is favoured .