The "in-in" Formalism and Cosmological Perturbations

Abstract

We describe an efficient scheme for evaluating higher order contributions to primordial cosmological perturbations using the "in-in" formalism, which is the basis of modern calculations of non-Gaussian and higher order contributions to the primordial spectrum. We show that diagrams with two or more vertices require careful handling. We present an implementation of the operator formalism in which these diagrams can be evaluated in a simple and transparent fashion. We illustrate our methodology by evaluating the correction to the primordial gravitational wave spectrum generated by scalar loops, a 2-vertex, 1-loop interaction. We then look at a generalized $N$-point, 2-vertex diagram.

9 pages. 2 figures. Minor revisions. Submitted to PRD

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• Quantum corrections to the primordial tensor spectrum: Open EFTs & Markovian decoupling of UV modes
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• CFTs Blueshift Tensor Fluctuations Universally
• On Holography in General Background and the Boundary Effective Action from AdS to dS
• Bound on Induced Gravitational Waves during Inflation Era
• In-in formalism for the entropy of quantum fields in curved spacetimes
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• Does decoherence violate decoupling?
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• Primordial Stochastic Gravitational Wave Background Anisotropies: in-in Formalization and Applications
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• First-order quantum correction to the Larmor radiation from a moving charge in a spatially homogeneous time-dependent electric field
• Non-perturbative analysis for a massless minimal quantum scalar with $V(\varphi )=\lambda {\varphi }^4/4!+\beta {\varphi }^3/3!$ in the inflationary de Sitter spacetime
• Particle detector models from path integrals of localized quantum fields
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• Late-time Structure of the Bunch-Davies FRW Wavefunction
• Quantum Larmor radiation from a moving charge in an electromagnetic plane wave background
• Primordial gravitational waves from excited states
• The Black Hole Window on Cosmic Inflation
• Manifestly Unitary Cosmological Perturbation Theory