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The Effective Field Theory of Multifield Inflation

Leonardo Senatore, Matias Zaldarriaga

TL;DR

This paper develops a universal Effective Field Theory framework for multifield inflation by coupling the Goldstone boson of time translation to additional light scalar fields that are either Goldstone-like or supersymmetry-protected. It constructs the most general Lagrangian consistent with diffeomorphism invariance and the protecting symmetries, and analyzes how horizon-crossing fluctuations map to curvature and isocurvature perturbations through a local, δN-like expansion. The authors identify a rich set of signatures, including a variety of three- and four-point non-Gaussianities, with the striking possibility that the four-point function can dominate in certain regimes, and show how observational patterns could distinguish between Abelian versus non-Abelian symmetry breaking or supersymmetric protection. The results provide a framework to connect detailed particle-theoretic symmetry structures to observable cosmological non-Gaussianity, offering new avenues to probe the underlying high-energy physics of inflation.

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.

The Effective Field Theory of Multifield Inflation

TL;DR

This paper develops a universal Effective Field Theory framework for multifield inflation by coupling the Goldstone boson of time translation to additional light scalar fields that are either Goldstone-like or supersymmetry-protected. It constructs the most general Lagrangian consistent with diffeomorphism invariance and the protecting symmetries, and analyzes how horizon-crossing fluctuations map to curvature and isocurvature perturbations through a local, δN-like expansion. The authors identify a rich set of signatures, including a variety of three- and four-point non-Gaussianities, with the striking possibility that the four-point function can dominate in certain regimes, and show how observational patterns could distinguish between Abelian versus non-Abelian symmetry breaking or supersymmetric protection. The results provide a framework to connect detailed particle-theoretic symmetry structures to observable cosmological non-Gaussianity, offering new avenues to probe the underlying high-energy physics of inflation.

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.

Paper Structure

This paper contains 13 sections, 138 equations, 1 figure, 2 tables.

Table of Contents

  1. Introduction
  2. Effective field theory of single-clock inflation
  3. Additional light scalar fields
  4. Abelian case ($N$-shift symmetries)
  5. Non-Abelian case
  6. Supersymmetric case
  7. Relating to curvature perturbations
  8. Isocurvature fluctuations
  9. Signatures
  10. Detectable four-point function from multi-field inflation
  11. Three-point function
  12. Isocurvature fluctuations and their non-Gaussianity
  13. Conclusions

Figures (1)

  • Figure 1: Representation of a typical multifield potential. Modes of interest for observation cross the horizon about sixty $e$-foldings before the end of inflation. Therefore, effects coming from the evolution of the filds after horizon crossing can be treated locally in real space. Our effective theory is more general than this example, as it does not assume that the inflaton is a scalar field. This example is however interesting in helping in visualizing the different scales in the problem.