The Effective Field Theory of Inflation (0709.0293v2)

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 paper establishes a unified EFT framework that systematically applies unitary gauge and Goldstone mode techniques to single-field inflation models.
• It details how symmetry breaking and higher-order operators capture key dynamics, such as variations in sound speed and non-Gaussian signals.
• The study links the theoretical framework to observables by predicting features like power spectrum tilt and offering constraints on non-Gaussianity parameters.

Overview of The Effective Field Theory of Inflation

The paper under consideration provides a comprehensive analysis of the Effective Field Theory (EFT) approach to single-field models of inflation. This methodology, well-established in particle physics, is adeptly applied to latent fluctuations around quasi de Sitter spaces, which characterize inflationary cosmologies. The authors—Cheung, Creminelli, Fitzpatrick, Kaplan, and Senatore—focus on the implications of broken time diffeomorphisms and utilize unitary gauge to build the most general theory incorporating the lowest-dimension operators. Their approach results in a unifying framework that accommodates a wide array of single-field inflationary models, ranging from standard slow-roll to scenarios with modified sound speeds and Ghost Inflation.

Key Insights and Formalism

1. Unitary Gauge and Operators: By transitioning to unitary gauge, where the scalar inflaton perturbations are absorbed by the metric, the authors systematically construct a Lagrangian with spatial diffeomorphism invariance. Notably, this involves terms like the extrinsic curvature of constant time surfaces and spatially diffeomorphic invariant operators, crucial for addressing the higher-order corrections to standard inflationary models.
2. Goldstone Boson Realization: In line with symmetry breaking paradigms, the scalar degree of freedom, transformed into a Goldstone boson, non-linearly realizes the broken time diffeomorphisms. This offers a transparent picture of long-wavelength modes and elucidates correlations such as reduced sound speed with increased non-Gaussian signal strength.
3. Applications to Inflationary Observables: The Lagrangian's framework predicts observable inflationary phenomena, such as the power spectrum's tilt, by highlighting its dependence on the Hubble rate and other slow-roll parameters. Additionally, it explores non-Gaussian features, projecting their size relative to the speed of sound and discriminating between various single-field models.

Numerical and Observational Implications

The paper presents strong numerical statements on the size and role of additional operators in the EFT framework. The magnitude and sign of operator coefficients are critical in avoiding instabilities, such as superluminal propagation, which challenges Lorentz invariance. Experimental constraints, notably on non-Gaussianity parameters $f_{NL}$, yield observable limitations on the sound speed, with implications for the ongoing and future CMB observations. For instance, reduced sound speeds directly relate to enhanced non-Gaussian signals—setting the threshold for $c_s$ notably above approximately 0.03, contingent on observable data.

Theoretical Extensions and Future Prospects

The authors propose directions for expanding the presented EFT formalism beyond single-field inflation. Notably, the methodology can be extended to quintessence and multi-field inflationary models, where understanding perturbations' behavior in different cosmological epochs remains critical. Moreover, connections to modified gravity theories, particularly in contexts violating the Null Energy Condition, are outlined, uncovering fertile grounds for further exploration.

Speculative Outlook

The pursuit of a more generalized framework that unifies diverse models under the EFT paradigm unquestionably broadens the theoretical landscape and aids in comparing inflationary predictions with empirical data. As experiments tighten constraints, this formalism stands as a robust foundation, paving the way for probing inflationary dynamics with newfound precision and possibly integrating additional fields or exploring non-canonical kinetic terms in future investigations.

In sum, the contributions of this paper lie in detailing the effective Lagrangian construction and using it to draw significant cosmological inferences. It addresses critical theoretical subtleties around symmetry breaking while placing practical bounds on the models through direct links to observational signatures.