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The Effective Field Theory of Inflation

Clifford Cheung, Paolo Creminelli, A. Liam Fitzpatrick, Jared Kaplan, Leonardo Senatore

TL;DR

The paper develops a comprehensive effective field theory framework for single-field inflation by describing fluctuations around a quasi de Sitter background in unitary gauge and then reintroducing the Goldstone mode π. The resulting action organizes all allowed high-energy corrections through a controlled set of operators, linking the background evolution to observable features such as the scalar power spectrum, tilt, and non-Gaussianities, with a key result being the intrinsic link between a reduced speed of sound and enhanced non-Gaussianity. It analyzes distinct regimes: vanilla slow-roll, small $c_s$ with sizable NG, and de Sitter-limit scenarios including Ghost Condensation, outlining decoupling limits, naturalness considerations, and observational constraints. The EFT approach thus provides a unifying language for diverse single-field inflationary models and a clear path to connect UV physics with cosmological data, while suggesting extensions to more complex scenarios such as quintessence and multi-field dynamics.

Abstract

We study the effective field theory of inflation, i.e. the most general theory describing the fluctuations around a quasi de Sitter background, in the case of single field models. The scalar mode can be eaten by the metric by going to unitary gauge. In this gauge, the most general theory is built with the lowest dimension operators invariant under spatial diffeomorphisms, like g^{00} and K_{mu nu}, the extrinsic curvature of constant time surfaces. This approach allows us to characterize all the possible high energy corrections to simple slow-roll inflation, whose sizes are constrained by experiments. Also, it describes in a common language all single field models, including those with a small speed of sound and Ghost Inflation, and it makes explicit the implications of having a quasi de Sitter background. The non-linear realization of time diffeomorphisms forces correlation among different observables, like a reduced speed of sound and an enhanced level of non-Gaussianity.

The Effective Field Theory of Inflation

TL;DR

The paper develops a comprehensive effective field theory framework for single-field inflation by describing fluctuations around a quasi de Sitter background in unitary gauge and then reintroducing the Goldstone mode π. The resulting action organizes all allowed high-energy corrections through a controlled set of operators, linking the background evolution to observable features such as the scalar power spectrum, tilt, and non-Gaussianities, with a key result being the intrinsic link between a reduced speed of sound and enhanced non-Gaussianity. It analyzes distinct regimes: vanilla slow-roll, small with sizable NG, and de Sitter-limit scenarios including Ghost Condensation, outlining decoupling limits, naturalness considerations, and observational constraints. The EFT approach thus provides a unifying language for diverse single-field inflationary models and a clear path to connect UV physics with cosmological data, while suggesting extensions to more complex scenarios such as quintessence and multi-field dynamics.

Abstract

We study the effective field theory of inflation, i.e. the most general theory describing the fluctuations around a quasi de Sitter background, in the case of single field models. The scalar mode can be eaten by the metric by going to unitary gauge. In this gauge, the most general theory is built with the lowest dimension operators invariant under spatial diffeomorphisms, like g^{00} and K_{mu nu}, the extrinsic curvature of constant time surfaces. This approach allows us to characterize all the possible high energy corrections to simple slow-roll inflation, whose sizes are constrained by experiments. Also, it describes in a common language all single field models, including those with a small speed of sound and Ghost Inflation, and it makes explicit the implications of having a quasi de Sitter background. The non-linear realization of time diffeomorphisms forces correlation among different observables, like a reduced speed of sound and an enhanced level of non-Gaussianity.

Paper Structure

This paper contains 12 sections, 77 equations.

Table of Contents

  1. Introduction
  2. Construction of the action in unitary gauge
  3. Action for the Goldstone Boson
  4. The various limits of single field inflation
  5. Slow-roll inflation and high energy corrections
  6. Small speed of sound and large non-Gaussianities
  7. Cutoff and Naturalness
  8. De-Sitter Limit and the Ghost Condensate
  9. De-Sitter Limit without the Ghost Condensate
  10. Conclusions
  11. The most general Lagrangian in unitary gauge
  12. Expanding around a given FRW solution