On the integration of fields and quanta in time dependent backgrounds

Abstract

Field theories with global continuous symmetries may admit configurations in which time translation invariance is broken by the movement of homogeneous background fields evolving along the flat directions implied by the symmetries. In this context, the field fluctuations along the broken symmetry are well parametrized by a Goldstone boson field that may non-trivially interact with other fields present in the theory. These interactions violate Lorentz invariance as a result of the broken time translation invariance of the background, producing a mixing between the field content and the particle spectrum of the theory. In this article we study the effects of such interactions on the low energy dynamics of the Goldstone boson quanta, paying special attention to the role of the particle spectrum of the theory. By studying the particular case of a canonical two-field model with a mexican-hat potential, we analyze the derivation of the low energy effective field theory for the Goldstone boson, and discuss in detail the distinction between integrating fields v/s integrating quanta, to finally conclude that they are equivalent. In addition, we discuss the implications of our analysis for the study of systems where time translation invariance is broken, such as cosmic inflation and time crystals.

38 pages, 1 figure

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• Cumulative effects in inflation with ultra-light entropy modes
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• On the Effective Field Theory for Quasi-Single Field Inflation
• Untangling features in the primordial spectra
• Inflation in Motion: Unitarity Constraints in Effective Field Theories with Broken Lorentz Symmetry
• Warm Quasi-Single Field Inflation
• A Tip for Landscape Riders: Multi-Field Inflation Can Fulfill the Swampland Distance Conjecture
• Consistency relations for sharp features in the primordial spectra
• Higher derivatives and power spectrum in effective single field inflation
• On degenerate models of cosmic inflation
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• Perturbative reduction of derivative order in EFT
• Non-Gaussianities in a two-field generalization of Natural Inflation
• Inflationary perturbation spectrum in extended effective field theory of inflation
• A Universal Bound on Excitations of Heavy Fields during Inflation
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• Primordial gravitational waves from excited states