Lectures on Open Effective Field Theories

TL;DR

This work introduces Open Effective Field Theories (Open EFTs) as a principled framework to model dissipation and noise in gravity and cosmology, extending traditional EFTs beyond collider-like, unitary settings. Central to the approach is the Schwinger-Keldysh (in-in) formalism, which doubles degrees of freedom and yields an open functional S_eff that contains unitary and non-unitary sectors, enabling model-agnostic treatments of environmental effects. The series develops concrete open EFTs for scalar fields, inflation, and electromagnetism, illustrating how integrating out heavy sectors generates Lamb-shift-like, dissipative, and stochastic contributions via their respective propagator structure (G^P, G^Δ, G^K) within the Keldysh basis. A key outcome is that dissipative and noise terms regularize otherwise singular behavior (e.g., folded singularities in correlators) and imprint characteristic non-Gaussian signatures in cosmology, with explicit connections to UV-complete models. The framework offers a systematic route to connect microscopic environmental physics to observable cosmological statistics, providing tools for power spectra and non-Gaussianities in open inflation and open EM, and highlighting the importance of locality, causality, and positivity constraints in open dynamics. Its open-EFT program paves the way for robust model-agnostic assessments of how hidden environments shape gravitational and electromagnetic observables across early- and late-time cosmology.

Abstract

Effective field theories offer a powerful method to unify diverse models under a small set of control parameters, allowing systematic expansions around well-established theories. These techniques, developed in particle physics, were designed for experiments where the initial state - the vacuum before a scattering event - is as clean and isolated as possible. Besides colliders, realistic environments are often noisy and dissipative. The recognition of the limitations of traditional EFT techniques has, over the past decade, sparked intense progress at the interface of high-energy physics and condensed matter. These considerations motivate a new approach to gravitation and cosmology, one that models the gravitational sector as evolving in the presence of an unobservable medium. Open Effective Field Theories provide a systematic and controllable field-theoretic framework for modeling dissipation and noise in gravitation and cosmology. These notes aim to introduce this versatile toolkit, enabling model-agnostic assessments of how unknown environments shape our observational probes.

Figures (22)

• Figure 1: Comparison between a) the single-branch path integral contour used in the computation of the wavefunction, and b) the double-branch path integral contour used in the computation of the density matrix. While the two approaches are equivalent in the case of pure states (see e.g. Donath:2024utn), the in-in contour also accomodates mixed states, which have no single-branch analogue.
• Figure 2: In-in diagrammatics of tree-level three-point correlator. The "$+$" and "$-$" diagram are related by complex conjugations for parity even interactions.
• Figure 3: In-in diagrammatics of tree-level $s$-channel four-point correlator with a massive exchange. The massless scalar $\varphi$ is represented in blue and the massive scalar $\sigma$ in orange.
• Figure 4: Illustration of the difference between amplitudes and correlators. In the in–out formalism, integrating out the heavy field produces a local effective action, while in the in–in framework it also gives rise to dissipative and stochastic operators involving odd powers of $1/M$.
• Figure 5: Schematic setup of open systems. The system, made of the degree of freedom $\zeta$, is embedded in the environment made of $\mathcal{F}$. Their interaction is specified by $g \widehat{H}_{\mathrm{int}}$. From the point of view of the system, this interaction renormalizes its energy level, generates energy loss through dissipation and information exchanges through noise. Figure adapted from manzanoShortIntroductionLindblad2020.