The δN formula is the dynamical renormalization group

Abstract

We derive the 'separate universe' method for the inflationary bispectrum, beginning directly from a field-theory calculation. We work to tree-level in quantum effects but to all orders in the slow-roll expansion, with masses accommodated perturbatively. Our method provides a systematic basis to account for novel sources of time-dependence in inflationary correlation functions, and has immediate applications. First, we use our result to obtain the correct matching prescription between the 'quantum' and 'classical' parts of the separate universe computation. Second, we elaborate on the application of this method in situations where its validity is not clear. As a by-product of our calculation we give the leading slow-roll corrections to the three-point function of field fluctuations on spatially flat hypersurfaces in a canonical, multiple-field model.

v1: 33 pages, plus appendix and references; 5 figures. v2: typographical typos fixed, minor changes to the main text and abstract, reference added; matches version published in JCAP

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Cited by in corpus (25)

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• Soft de Sitter Effective Theory
• Numerical evaluation of the bispectrum in multiple field inflation
• Primordial non-Gaussianity from ultra slow-roll Galileon inflation
• Evading no-go for PBH formation and production of SIGWs using Multiple Sharp Transitions in EFT of single field inflation
• Large fluctuations and Primordial Black Holes
• The squeezed limit of the bispectrum in multi-field inflation
• The effects of a fast-turning trajectory in multiple-field inflation
• The hemispherical asymmetry from a scale-dependent inflationary bispectrum
• Obviating PBH overproduction for SIGWs generated by Pulsar Timing Arrays in loop corrected EFT of bounce
• \bf $\delta M$ Formalism: A New Approach to Cosmological Perturbation Theory in Anisotropic Inflation
• Regularized-Renormalized-Resummed loop corrected power spectrum of non-singular bounce with Primordial Black Hole formation
• Untangling PBH overproduction in $w$-SIGWs generated by Pulsar Timing Arrays for MST-EFT of single field inflation
• Primordial Black Holes from Effective Field Theory of Stochastic Single Field Inflation at NNNLO
• Quantum quenches during inflation
• Introduction to the number of $e$-folds in slow-roll inflation
• Negative non-Gaussianity as a salvager for PBHs with PTAs in bounce
• $\Delta N$ Formalism and Conserved Currents in Cosmology
• Stochastic origin of primordial fluctuations in the Sky
• Optimal bispectrum constraints on single-field models of inflation
• RRR fluctuations from non-singular bounce
• Non-Gaussianity in D3-brane inflation