Effective Field Theory of Multi-Field Inflation a la Weinberg

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employ the effective field theory approach for multi-field inflation which is a
generalization of Weinberg's work. In this method the first correction terms in
addition to standard terms in the Lagrangian have been considered. These terms
contain up to the fourth derivative of the fields including the scalar field
and the metric. The results show the possible shapes of the interaction terms
resulting eventually in non-Gaussianity in a general formalism. In addition
generally the speed of sound is different but almost unity. Since in this
method the adiabatic mode is not discriminated initially so we define the
adiabatic as well as entropy modes for a specific two-field model. It has been
shown that the non-Gaussianity of the adiabatic mode and the entropy mode are
correlated in shape and amplitude. It is shown that even for speed close to
unity large non-Gaussianities are possible in multi-field case. The amount of
the non-Gaussianity depends on the curvature of the classical path in the
phase-space in the Hubble unit such that it is large for the large curvature.
In addition it is emphasized that the time derivative of adiabatic and entropy
perturbations do not transform due to the shift symmetry as well as the
original perturbations. Though two specific combinations of them are invariant
under such a symmetry and these combinations should be employed to construct an
effective field theory of multi-field inflation.