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Reconstructing the EFT of Inflation from Cosmological Data
by Amel Durakovic, Paul Hunt, Subodh P. Patil, Subir Sarkar
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Submission summary
Authors (as registered SciPost users):  Subodh Patil · Subir Sarkar 
Submission information  

Preprint Link:  https://arxiv.org/abs/1904.00991v1 (pdf) 
Date submitted:  20190402 02:00 
Submitted by:  Patil, Subodh 
Submitted to:  SciPost Physics 
Ontological classification  

Academic field:  Physics 
Specialties: 

Approach:  Theoretical 
Abstract
Reconstructions of the primordial power spectrum (PPS) of curvature perturbations from cosmic microwave background anisotropies and largescale structure data suggest that the usually assumed powerlaw 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 Einsteinde 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 2ndorder 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 slowroll 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. Thus we provide a dictionary (more accurately, a thesaurus) to go from observational data, via the reconstructed PPS, to models that reproduce them to per cent level precision.
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Reports on this Submission
Anonymous Report 1 on 2019529 (Invited Report)
 Cite as: Anonymous, Report on arXiv:1904.00991v1, delivered 20190529, doi: 10.21468/SciPost.Report.981
Strengths
1. Wellwritten and explained
2. Valuable result allowing accurate (percent level) reconstruction of potential features in the primordial power spectrum from (singleclock) EFT models of inflation
3. Good and clear analytic toymodel examples providing proof of principle
Weaknesses
1. Discussion of the phase transitions and in particular the additional sharp oscillations that need to be introduced for the Einsteinde Sitter background results.
2. Explanation and discussion of the leading order corrections to the potential
Report
I enjoyed reading this paper, which is wellwritten and very clear. The authors show convincingly that they can reconstruct, to second order, estimated features in the primordial power spectrum from time dependent parameters in and EFT description of singleclock models of inflation. First establishing the relations to second order in the features, they apply their method to an analytic toy model example, providing a proof of principle. They then apply their method to a LambdaCDM and Einsteinde Sitter background model, resulting in 2ndorder reconstructed slowroll epsilon parameters and the inflationary potential. Their method is a valuable contribution that will allow a more precise reconstruction of (and further constrain the presence of) features, assuming a particular background model. I would have appreciated a more elaborate discussion on the meaning and implications of the reconstruction in the Einsteinde Sitter case, where the result for the slowroll parameter has more finestructure and in particular seems to require a sharp oscillation over less than a single efold. To explain better how the (claimed) significance of this sharp oscillation compares to the (larger) bumps would be useful. In the discussion, which is very brief, the authors introduce an example of leading order adiabatic corrections to the effective potential that might give rise to the reconstructed features. This paragraph would benefit from a bit more context (instead of just referring to the appendix) and a more specific discussion with respect to the two background scenario's discussed (\Lambda CDM versus Einsteinde Sitter).
Besides these relatively minor points, which I would like to see addressed, I would recommend the manuscript to be published.
Requested changes
1. Address the significance of the sharp oscillation in the Einsteinde Sitter scenario
2. Expand the discussion on the leading corrections to the effective potential and in particular what that means for the \Lambda CDM and Einsteinde Sitter background results
Author: Subodh Patil on 20190716 [id 563]
(in reply to Report 1 on 20190529)We are grateful to the Referee for the encouraging and helpful comments.
We have noted the concern regarding the significance of the fine structure in our reconstructed slow roll parameters and accordingly reexamined our procedure for estimating the error bands. This turned out to be an important exercise because we realised that we had underestimated them by considering only the diagonal elements of the frequentist covariance matrix which describes the error in the reconstructed PPS. We have now repeated our calculations using the the full covariance matrix and find a much enlarged error band. (All this took some time hence the delay in responding  however this is not yet a complete analysis which would require evaluating the full likelihood … which is beyond the scope of the present work.) We have attached a note which shows graphically the significant correlations at both high and low wave numbers which result in the enlarged uncertainties.
This of course does not undermine our main result which is to demonstrate accurate EFT parameter reconstruction from a cosmological data set. It does however enable us to (hopefully) adequately address the Referee’s remark that “… in the Einsteinde Sitter case … the result for the slowroll parameter has more finestructure and in particular seems to require a sharp oscillation over less than a single efold. To explain better how the (claimed) significance of this sharp oscillation compares to the (larger) bumps would be useful”. We agree and have now added explanatory text to both “1. Address the significance of the sharp oscillation in the Einsteinde Sitter scenario” as well as to "2. Expand the discussion on the leading corrections to the effective potential and in particular what that means for the \Lambda CDM and Einsteinde Sitter background results” as the Referee has requested.
For ease of identifying the added sections we have marked these in blue in the attached manuscript (including some additional references). We hope the Referee is satisfied with these clarifications and our revised manuscript can now be published in SciRep.
Attachment:
note_changes_highlighted.pdf