Primordial power spectrum features in phenomenological descriptions of inflation

In this paper, 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 three 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. In the context of the phenomenological description studied here, the sound speed of the primordial curvature perturbation is found to be $c_s> 0.2$ at $95\%$~CL for a number of $e$-folds $N=60$. Within this parametrization, we discard scale invariance with a significance of about $10\sigma$, and the running of the spectral index is constrained as $\alpha_s=-0.62\,^{+0.08}_{-0.09} \times 10^{-3}$. The limit on the tensor-to-scalar ratio is $r<0.003$ at $95\%$~CL from CMB data alone. The maximum amplitude of the equilateral non-gaussianity that we obtain, $|f^{\text{equil}}_{\text{NL}}|\sim 2$, is much smaller than the current Planck mission errors. Future high-redshift, all-sky surveys could reach the required accuracy on equilateral non-gaussianities to allow for additional and independent tests of the parametrization explored here.