CMB from EFT

TL;DR

This paper employs an Effective Field Theory framework to compute and analyze the correlation functions of primordial fluctuations in a quasi de Sitter universe, connecting theoretical predictions with CMB observations.

Contribution

It introduces a systematic EFT approach to calculate scalar and tensor correlations for arbitrary initial vacua, linking EFT coefficients to inflationary parameters and observational data.

Findings

Computed two-point and three-point correlations in EFT framework.

Constrained EFT operator coefficients using Planck CMB data.

Validated EFT predictions against canonical single-field models.

Abstract

In this work, we study the key role of generic Effective Field Theory (EFT) framework to quantify the correlation functions in a quasi de Sitter background for an arbitrary initial choice of the quantum vacuum state. We perform the computation in unitary gauge, in which we apply the St$\ddot{\text{u}}$ckelberg trick in lowest dimensional EFT operators which are broken under time diffeomorphism. In particular, using this non-linear realization of broken time diffeomorphism and truncating the action by considering the contribution from two derivative terms in the metric, we compute the two-point and three-point correlations from scalar perturbations and two-point correlation from tensor perturbations to quantify the quantum fluctuations observed in the Cosmic Microwave Background (CMB) map. We also use equilateral limit and squeezed limit configurations for the scalar three-point correlations in Fourier space. To give future predictions from EFT setup and to check the consistency of our derived results for correlations, we use the results obtained from all classes of the canonical single-field and general single-field $P(X,\phi)$ model. This analysis helps us to fix the coefficients of the relevant operators in EFT in terms of the slow-roll parameters and effective sound speed. Finally, using CMB observations from Planck we constrain all these coefficients of EFT operators for the single-field slow-roll inflationary paradigm.