# Reconstructing the EFT of Inflation from Cosmological Data

### Submission summary

 As Contributors: Subodh Patil · Subir Sarkar Arxiv Link: https://arxiv.org/abs/1904.00991v1 (pdf) Date submitted: 2019-04-02 02:00 Submitted by: Patil, Subodh Submitted to: SciPost Physics Academic field: Physics Specialties: High-Energy Physics - Theory High-Energy Physics - Phenomenology Cosmology and Nongalactic Astrophysics Approach: Theoretical

### Abstract

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. 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.

### Ontology / Topics

See full Ontology or Topics database.

###### Current status:
Has been resubmitted

### Submission & Refereeing History

#### Published as SciPost Phys. 7, 049 (2019)

Resubmission 1904.00991v2 on 16 July 2019

Submission 1904.00991v1 on 2 April 2019

## Reports on this Submission

### Anonymous Report 1 on 2019-5-29 (Invited Report)

• Cite as: Anonymous, Report on arXiv:1904.00991v1, delivered 2019-05-29, doi: 10.21468/SciPost.Report.981

### Strengths

1. Well-written and explained
2. Valuable result allowing accurate (percent level) reconstruction of potential features in the primordial power spectrum from (single-clock) EFT models of inflation
3. Good and clear analytic toy-model 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 Einstein-de Sitter background results.
2. Explanation and discussion of the leading order corrections to the potential

### Report

I enjoyed reading this paper, which is well-written 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 single-clock 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 Lambda-CDM and Einstein-de Sitter background model, resulting in 2nd-order reconstructed slow-roll 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 Einstein-de Sitter case, where the result for the slow-roll parameter has more fine-structure and in particular seems to require a sharp oscillation over less than a single e-fold. 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 Einstein-de 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 Einstein-de 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 Einstein-de Sitter background results

• validity: high
• significance: good
• originality: ok
• clarity: high
• formatting: good
• grammar: excellent

### Author:  Subodh Patil  on 2019-07-16  [id 563]

(in reply to Report 1 on 2019-05-29)
Category: