We constrain slow-roll inflationary models using the recent WMAP data combined with data from the VSA , CBI , ACBAR and 2dF experiments .
We find the slow-roll parameters to be 0 < \epsilon _ { 1 } < 0.032 and \epsilon _ { 2 } +5.0 \epsilon _ { 1 } = 0.036 \pm 0.025 .
For inflation models V \propto \phi ^ { \alpha } we find that \alpha < 3.9 , 4.3 at the 2 \sigma and 3 \sigma levels , indicating that the \lambda \phi ^ { 4 } model is under very strong pressure from observations .
We define a convergence criterion to judge the necessity of introducing further power spectrum parameters such as the spectral index and running of the spectral index .
This criterion is typically violated by models with large negative running that fit the data , indicating that the running can not be reliably measured with present data .