The primordial power spectrum (PPS) describes the variance of curvature perturbations on different scales. It is often assumed to be a power law without features, almost scale invariant, a prediction of simple inflationary models. The curvature fluctuations are imprinted on the temperature fluctuations of the cosmic microwave background (CMB) and so, knowing the CMB and the cosmological parameters, the PPS can be reconstructed. The estimated PPS is sensitive to the assumed cosmological parameters. While the introduction of characteristic scales in the PPS are almost a luxury when the standard ACDM cosmological model is assumed, they are necessary for good fits to data assuming alternative cosmological models such as Einstein-de Sitter (EdS) which requires a bump in the spectrum. The lack of a fundamental understanding of dark energy motivates this case and as the inflationary stage is the least accessible, it seems early to commit to a restrictive power-law parameterisation. Here, a bidirectional dictionary is developed between features in a PPS and changes in the slow-roll parameter, or the speed of sound, which are parameters in the secondorder action of the effective field theory (EFT) of inflation. The change in the slow-roll parameter is found to relate to the derivative of the sine transform of the PPS, just as the gravitational potential relates to the mass density in Newtonian gravity. This makes it possible to summarise the needed features in terms of EFT parameters without committing to a particular inflationary scenario. Reconstructions of EFT parameters from the reconstructed PPS are performed, and the direct reconstruction of EFT parameters from CMB or other data is discussed. Here, an isotropy test of the PPS estimated from the Planck PR2 SMICA map is performed, testing for a non-zero quadrupole modulation. Statistical tests of the quadrupole modulation are unusual at 2:1 significance level when testing only the amplitude of the quadrupole, but 6:95 when using a test sensitive to direction also. Best-fit scaleindependent quadrupole modulations point near the Galactic Plane or perpendicular to it suggesting contamination by Galactic foregrounds. On large scales, the quadrupole modulation points in a direction perpendicular to the CMB dipole and may be aligned with the hemispherical asymmetry. Here, a test statistic is generalised that can be used to put constraints on cosmological parameters that are almost independent of the PPS. It requires the use of two data sets that depend differently on the PPS, such as temperature and polarisation. The capacity of two data sets to rule out cosmological parameters is discussed.