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 Stückelberg 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 , ϕ ) 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.
Highlights
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 have derived the analytical expressions for the two-point correlation function for scalar and tensor fluctuations and three-point correlation function for scalar fluctuations from EFT framework in quasi de Sitter background in a model-independent way
During our computation, we have truncated the EFT action by considering the all possible two derivative terms in the metric. This allows us to derive correct expressions for the two-point and three-point correlation functions for EFT which are consistent with both the single-field slow-roll model and generalized non-canonical P(X, φ) single-field models minimally coupled with gravity28
Summary
The basic idea of Effective Field Theory (EFT) is very useful in many branches in theoretical physics including particle physics [1,2], condensed matter physics [3], gravity [4,5], cosmology [6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26] and hydrodynamics [27,28]. Top-down approach: In this case, the usual idea is to start with a UV complete fundamental QFT framework which contain all possible degrees of freedom Using this setup one can derive the Universe 2019, 5, 155; doi:10.3390/universe5060155 www.mdpi.com/journal/universe. Oγ(j)[φ]∀γ, ∀j = 1, 2, · · · , N represent ∆γ mass dimensional local EFT operators suppressed by the scale MΨ∆γj −4 In this connection one of the best possible example of UV complete field theoretic setup is string theory from which one can derive an EFT setup at the string scale Λs which is identified with MΨj in Equation (3)
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