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S. Weinberg, “Effective Field Theory for Inflation,” Phys. Rev. D 77
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A. Achucarro, J. O. Gong, G. A. Palma and S. P. Patil, “Correlating features in the primordial spectra,” Phys. Rev. D 87
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2013
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C. P. Burgess, M. W. Horbatsch and S. P. Patil, “Inflating in a Trough: Single-Field Effective Theory from Multiple-Field Curved Valleys,” JHEP 1301
Original
2013
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P. Hunt and S. Sarkar, “Reconstruction of the primordial power spectrum of curvature perturbations using multiple data sets,” JCAP 1401
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2019

Reconstructing the EFT of Inflation from Cosmological Data

Durakovic, Amel, Hunt, Paul, Patil, Subodh P. et al.

Understand

Reconstructions of the primordial power spectrum (PPS) of curvature perturbations from cosmic microwave background anisotropies and large-scale structure data suggest that the usually assumed power-law PPS has localised features (up to $\sim 10\%$ in amplitude), although of only marginal significance in the framework of $\Lambda$CDM cosmology.

On the other hand if the underlying cosmology is assumed to be Einstein-de Sitter, larger features in the PPS (up to $\sim 20\%$) are required to accurately fit the observed acoustic peaks.
Within the context of single clock inflation, we show that any given reconstruction of the PPS can be mapped on to functional parameters of the underlying effective theory of the adiabatic mode within a 2nd-order formalism, provided the best fit fractional change of the PPS, $\Delta\mathcal{P}_\mathcal{R}/\mathcal{P}_\mathcal{R}$ is such that $(\Delta\mathcal{P}_\mathcal{R}/\mathcal{P}_\mathcal{R})^3$ falls within the $1\,\sigma$ confidence interval of the reconstruction for features induced by variations of either the sound speed $c_\mathrm{s}$ or the slow-roll parameter $\epsilon$.
Although there is a degeneracy amongst these functional parameters (and the models that project onto them), we can identify simple representative inflationary models that yield such features in the PPS.