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Cancellation of loop corrections to soft scalar power spectrum

Yohei Ema, Muzi Hong, Ryusuke Jinno, Kyohei Mukaida

Abstract

We prove the absence of scale-invariant one-loop corrections to the superhorizon curvature perturbations from small-scale (potentially enhanced) scalar perturbations in a general inflationary setup, including the transient ultra-slow-roll scenario. We demonstrate this by analyzing the symmetry structure of an in-in effective field theory for the soft curvature perturbations, and by explicitly performing one-loop calculations, integrating out hard modes in the soft limit of external momenta. The dilatation symmetry, respected by a counter term necessary for the tadpole cancellation, guarantees the cancellation of scale-invariant corrections.

Cancellation of loop corrections to soft scalar power spectrum

Abstract

We prove the absence of scale-invariant one-loop corrections to the superhorizon curvature perturbations from small-scale (potentially enhanced) scalar perturbations in a general inflationary setup, including the transient ultra-slow-roll scenario. We demonstrate this by analyzing the symmetry structure of an in-in effective field theory for the soft curvature perturbations, and by explicitly performing one-loop calculations, integrating out hard modes in the soft limit of external momenta. The dilatation symmetry, respected by a counter term necessary for the tadpole cancellation, guarantees the cancellation of scale-invariant corrections.
Paper Structure (19 sections, 146 equations, 1 figure)

This paper contains 19 sections, 146 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Lightning review of in-in formalism in Keldysh $r/a$-basis
  3. Keldysh $r/a$-basis
  4. Soft-limit of bulk-to-boundary propagator
  5. Soft $\zeta$ EFT on in-in contour
  6. Soft $\zeta$ EFT and dilatation
  7. Tadpole cancellation and absence of soft fully retarded correlators
  8. Absence of scale-invariant corrections
  9. Explicit calculation of soft $\zeta$ EFT
  10. Toy model with a spectator field
  11. Toy model of curvature perturbation
  12. Arbitrary interactions
  13. Conclusion
  14. Acknowledgements
  15. Bulk-to-boundary propagator in transient ultra slow-roll inflation
  16. ...and 4 more sections

Figures (1)

  • Figure 1: The path integral contour of the in-in formalism for the cosmological correlators. We evaluate the correlation functions of the curvature perturbation at the future infinity, which corresponds to the end of inflation.