Derivative Interactions during Inflation: A Systematic Approach

Abstract

We present a systematic prescription for calculating cosmological correlation functions for models with derivative interactions through the wavefunction of the universe and compare this result with the "in-in" formalism -- canonical approach. The key step in this procedure is to perform the path integral over conjugate momenta after which a straightforward generalisation of Feynman's Rules can be applied. We show that this integral recovers the classical action plus some additional divergent contributions which are necessary to cancel other divergences that arise due to loop diagrams involving time derivatives. As a side project, for the first time, we introduce the "off-shell" version of the in-in formalism that is sometimes more straightforward, especially for the models with derivative coupling. To examine our prescription, as a specific example, we work out the trispectra of the scalar fluctuation in the model with the $\lambda {{\varphi }^{\prime }}^3$ derivative coupling.

arXiv comment19+23 pages, 7 figures

References in corpus (22)

• Non-Gaussian features of primordial fluctuations in single field inflationary models
• The Effective Field Theory of Inflation
• Observational Signatures and Non-Gaussianities of General Single Field Inflation
• Quantum Contributions to Cosmological Correlations
• Primordial Non-Gaussianities from Inflation Models
• Quasi-Single Field Inflation and Non-Gaussianities
• Non-Gaussianities in Single Field Inflation and their Optimal Limits from the WMAP 5-year Data
• Signatures of Supersymmetry from the Early Universe
• On Soft Limits of Inflationary Correlation Functions
• The Quantum Gravitational Back-Reaction On Inflation
• The Cosmological Bootstrap: Weight-Shifting Operators and Scalar Seeds
• The Cosmological Optical Theorem
• Schwinger-Keldysh Diagrammatics for Primordial Perturbations
• Multiple field inflation
• Productive Interactions: heavy particles and non-Gaussianity
• On the full trispectrum in single field DBI-inflation
• Field redefinitions in effective theories at higher orders
• Large Primordial Trispectra in General Single Field Inflation
• Path Integral for Inflationary Perturbations
• Path integral for multi-field inflation
• New natural shapes of non-Gaussianity from high-derivative interactions and their optimal limits from WMAP 9-year data
• Symmetry Factors of Feynman Diagrams for Scalar Fields

Cited by in corpus (1)

• Cosmological Bootstrap in Slow Motion