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 parameterization, we discard scale invariance with a significance of about 10σ, and the running of the spectral index is constrained as α_s=−0.60_−0.10 ^+0.08×10⁻³ (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_NL ^equil|<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.