Small field models with gravitational wave signature supported by CMB data

We study scale dependence of the cosmic microwave background (CMB) power spectrum in a class of small, single-field models of inflation which lead to a high value of the tensor to scalar ratio. The inflaton potentials that we consider are degree 5 polynomials, for which we precisely calculate the power spectrum, and extract the cosmological parameters: the scalar index $n_s$, the running of the scalar index $n_{\mathrm{run}}$ and the tensor to scalar ratio $r$. We find that for non-vanishing $n_{\mathrm{run}}$ and for $r$ as small as $r=0.001$, the precisely calculated values of $n_s$ and $n_{\mathrm{run}}$ deviate significantly from what the standard analytic treatment predicts. We study in detail, and discuss the probable reasons for such deviations. As such, all previously considered models (of this kind) are based upon inaccurate assumptions. We scan the possible values of potential parameters for which the cosmological parameters are within the allowed range by observations. The 5 parameter class is able to reproduce all of the allowed values of $n_s$ and $n_{\mathrm{run}}$ for values of $r$ that are as high as 0.001. Subsequently this study at once refutes previous such models built using the analytical Stewart-Lyth term, and revives the small field brand, by building models that do yield an appreciable $r$ while conforming to known CMB observables.