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Recent cosmological observations hint at a deviation from the simplepower-law form of the primordial spectrum of curvature perturbations. In thispaper we show that in the presence of a tensor component, a turn-over in theinitial spectrum is preferred by current observations, and hence non-power-lawmodels ought to be considered. For instance, for a power-law parameterisationwith both a tensor component and running parameter, current data show apreference for a negative running at more than $2.5\sigma$ C.L. As aconsequence of this deviation from a power-law, constraints on thetensor-to-scalar ratio $r$ are slightly broader. We also present constraints onthe inflationary parameters for a model-independent reconstruction and theLasenby & Doran (LD) model. In particular, the constraints on thetensor-to-scalar ratio from the LD model are: $r_{\rm LD}=0.11\pm{0.024}$. Inaddition to current data, we show expected constraints from Planck-like andCMB-Pol sensitivity experiments by using Markov-Chain-Monte-Carlo samplingchains. For all the models, we have included the Bayesian Evidence to perform amodel selection analysis. The Bayes factor, using current observations, shows astrong preference for the LD model over the standard power-lawparameterisation, and provides an insight into the accuracy of differentiatingmodels through future surveys.

Constraints on the Tensor-to-Scalar ratio for non-power-law models