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.
