CMB from EFT
  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.
