Effective theories of single field inflation when heavy fields matter (1201.6342v2)

Abstract: We compute the low energy effective field theory (EFT) expansion for single-field inflationary models that descend from a parent theory containing multiple other scalar fields. By assuming that all other degrees of freedom in the parent theory are sufficiently massive relative to the inflaton, it is possible to derive an EFT valid to arbitrary order in perturbations, provided certain generalized adiabaticity conditions are respected. These conditions permit a consistent low energy EFT description even when the inflaton deviates off its adiabatic minimum along its slowly rolling trajectory. By generalizing the formalism that identifies the adiabatic mode with the Goldstone boson of this spontaneously broken time translational symmetry prior to the integration of the heavy fields, we show that this invariance of the parent theory dictates the entire non-perturbative structure of the descendent EFT. The couplings of this theory can be written entirely in terms of the reduced speed of sound of adiabatic perturbations. The resulting operator expansion is distinguishable from that of other scenarios, such as standard single inflation or DBI inflation. In particular, we re-derive how certain operators can become transiently strongly coupled along the inflaton trajectory, consistent with slow-roll and the validity of the EFT expansion, imprinting features in the primordial power spectrum, and we deduce the relevant cubic operators that imply distinct signatures in the primordial bispectrum which may soon be constrained by observations.

• The paper constructs a comprehensive EFT for single-field inflation by integrating out heavy fields under strict adiabaticity conditions.
• It demonstrates that a reduced speed of sound crucially modulates inflaton dynamics and the emergence of non-Gaussian signatures.
• Observable imprints in the primordial power spectrum and bispectrum provide vital tests for future CMB and large-scale structure surveys.

Effective Theories of Single Field Inflation When Heavy Fields Matter

The paper in question explores the effective field theory (EFT) framework for analyzing single-field inflationary models derived from a multifield parent theory. In this context, it examines cases where the additional scalar fields, or "heavy fields," are adequately massive compared to the inflaton, enabling their integration out to produce a low-energy effective theory.

Core Contributions and Methodology

The authors introduce several notable advances in the theoretical understanding of multifield inflation:

1. EFT Construction: The paper provides a comprehensive methodology for constructing the EFT of single-field inflation. By assuming a hierarchy in the mass spectrum where heavy fields are much heavier than the inflaton, it proposes an EFT expansion valid to all perturbative orders, given specific adiabaticity conditions.
2. Generalized Adiabaticity Conditions: The paper highlights conditions under which a low-energy EFT is valid, even when the inflaton deviates from its adiabatic minimum along a trajectory that exhibits slow roll. These conditions constrain the system to allow consistent EFT descriptions without exciting the integrated-out heavy modes.
3. Influence of Heavy Fields: The presence of massive fields affects the dynamics of the inflaton through non-trivial interactions. Utilizing a formal framework, the authors show that the reduced speed of sound of adiabatic perturbations serves as a pivotal parameter, regulating the couplings in the EFT. The integration reveals transiently strong couplings for certain operators, contingent on the inflaton dynamics.
4. Observable Implications: The effects of heavy fields manifest as features in the primordial power spectrum and distinctive signatures in the bispectrum. Importantly, by rederiving specific cubic operators, the paper links these theoretical predictions to observational constraints expected from future cosmic microwave background (CMB) and large-scale structure data analyses.
5. Minkowski and Inflationary Frameworks: The techniques and findings are contextualized in both a simplified Minkowski spacetime and a full inflationary framework, demonstrating the consistent emergence of the reduced speed of sound as a determinant in these distinct setups.

Implications and Future Directions

The findings of this paper have several important implications:

• Constraining Inflationary Models: The results offer a framework for constraining inflationary models using EFT techniques, potentially narrowing down viable theories consistent with observational data.
• Non-Gaussianities: The derivation of non-Gaussian signatures provides a vital link between theoretical predictions and potential observational features, reinforcing the utility of CMB experiments in testing multifield dynamics during inflation.
• Beyond Single-Field Models: By demonstrating the effective role of heavy fields, the research encourages a broader exploration of multifield effects, challenging the conventional single-field inflation paradigm.
• Theoretical Generalization: The treatment of adiabaticity transcends conventional interpretations, suggesting avenues to further generalize to other multifield scenarios or complex field-space geometries.

Future research could extend this analysis to more complicated multifield setups, explore loop corrections in the resulting EFT, and further sharpen the theoretical predictions with experimental data from ongoing and future astrophysical surveys. Overall, this work underscores the profound impact of heavy fields on inflationary dynamics and the utility of EFT in contemporary cosmological contexts.