Primordial power spectrum features in phenomenological descriptions of inflation

We extend an alternative, phenomenological approach to inflation by means of an equation of state and a sound speed, both of them functions of the number of $e$-folds and four phenomenological parameters. This approach captures a number of possible inflationary models, including those with non-canonical kinetic terms or scale-dependent non-gaussianities. We perform Markov Chain Monte Carlo analyses using the latest cosmological publicly available measurements, which include Cosmic Microwave Background (CMB) data from the Planck satellite. Within this parametrization, we discard scale invariance with a significance of about $10\sigma$, and the running of the spectral index is constrained as $\alpha_s=-0.60\,^{+0.08}_{-0.10}\times 10^{-3}$ ($68\%$~CL errors). The limit on the tensor-to-scalar ratio is $r<0.005$ at $95\%$~CL from CMB data alone. We find no significant evidence for this alternative parameterization with present cosmological observations. The maximum amplitude of the equilateral non-gaussianity that we obtain, $|f^{\text{equil}}_{\text{NL}}|< 1$, is much smaller than the current Planck mission errors, strengthening the case for future high-redshift, all-sky surveys, which could reach the required accuracy on equilateral non-gaussianities.

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