Recent cosmological observations hint at a deviation from the simple power-law form of the primordial spectrum of curvature perturbations .
In this paper we show that in the presence of a tensor component , a turn-over in the initial spectrum is preferred by current observations , and hence non-power-law models ought to be considered .
For instance , for a power-law parameterisation with both a tensor component and running parameter , current data show a preference for a negative running at more than 2.5 \sigma C.L .
As a consequence of this deviation from a power-law , constraints on the tensor-to-scalar ratio r are slightly broader .
We also present constraints on the inflationary parameters for a model-independent reconstruction and the Lasenby & Doran ( LD ) model .
In particular , the constraints on the tensor-to-scalar ratio from the LD model are : r _ { LD } = 0.11 \pm { 0.024 } .
In addition to current data , we show expected constraints from Planck-like and CMB-Pol sensitivity experiments by using Markov-Chain-Monte-Carlo sampling chains .
For all the models , we have included the Bayesian Evidence to perform a model selection analysis .
The Bayes factor , using current observations , shows a strong preference for the LD model over the standard power-law parameterisation , and provides an insight into the accuracy of differentiating models through future surveys .