Abstract
Abstract We generalize the Effective Field Theory of Inflation to include additional light scalar degrees of freedom that are in their vacuum at the time the modes of interest are crossing the horizon. In order to make the scalars light in a natural way we consider the case where they are the Goldstone bosons of a global symmetry group or are partially protected by an approximate supersymmetry. We write the most general Lagrangian that couples the scalar mode associated to the breaking of time translation during inflation to the additional light scalar fields. This Lagrangian is constrained by diffeomorphism invariance and the additional symmetries that keep the new scalars light. This Lagrangian describes the fluctuations around the time of horizon crossing and it is supplemented with a general parameterization describing how the additional fluctuating fields can affect cosmological perturbations. We find that multifield inflation can reproduce the non-Gaussianities that can be generated in single field inflation but can also give rise to new kinds of non-Gaussianities. We find several new three-point function shapes. We show that in multifield inflation it is possible to naturally suppress the three-point function making the four-point function the leading source of detectable non-Gaussianities. We find that under certain circumstances, i.e. if specific shapes of non-Gaussianities are detected in the data, one could distinguish between single and multifield inflation and sometimes even among the various mechanisms that kept the additional fields light.
Highlights
General theory is built with the lowest dimension operators invariant under spatial diffeomorphisms, like g00, and Kμν, the extrinsic curvature of constant time surfaces
We find that multifield inflation can reproduce the non-Gaussianities that can be generated in single field inflation but can give rise to new kinds of nonGaussianities
This approach can be used to translate the constraints on the non-Gaussianities obtained from WMAP data directly onto parameters of the Lagrangian for the fluctuations without any loss of generality [3]. It is the Lagrangian for the fluctuations that is directly tested by cosmological observations. This approach of using the experimental data to put constraints on the most generic Lagrangian built with the lowest dimensional operators compatible with the symmetries is well established in the particle physics community, where it goes under the name of Precision Electroweak Tests [10, 11], but it is quite new in the cosmological setting
Summary
We briefly review the effective action for single-clock inflation. This effective action was developed in [1, 6] and we refer the reader to those papers for a detailed explanation. Dots represent operators that start at higher order in the perturbations or in derivatives This is the most general action for single field inflation and it is unique [1]. The unitary gauge Lagrangian describes three degrees of freedom: the two graviton helicities and a scalar mode This mode will become explicit after one performs a broken time diffeomorphism (Stuckelberg trick) to reintroduce the Goldstone boson which non-linearly realizes this symmetry. If we are interested just in effects that are not dominated by the mixing with gravity, we can neglect the metric perturbations and just keep the π fluctuations In this regime, a term of the form g00 in the unitary gauge Lagrangian becomes:. This is the exact analogous of what happens for data from particle accelerators when the precision electroweak tests of the Standard Model are carried out [10, 11]
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