Constraining slow-roll inflation with WMAP and 2dF

We constrain slow-roll inflationary models using the recent Wilkinson Microwave Anisotropy Probe data combined with data from the VSA, CBI, ACBAR and 2dF experiments. We find the slow-roll parameters to be $0<\mathrm{}{\epsilon }_1<0.032\mathrm{}$ and ${\epsilon }_2+5.0\mathrm{}{\epsilon }_1=0.036\mathrm{}\pm \mathrm{0.025.}$ For inflation models $V\propto {\phi }^{\alpha }$ we find that $\alpha <3.9,4.3\mathrm{}$ 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 cannot be reliably measured with present data.