The Disordered Universe 2025: Open Effective Field Theories

Abstract

Effective field theories (EFTs) offer a powerful method to unify diverse models under a small set of control parameters, allowing systematic expansions around well-established theories. While these techniques were traditionally developed for particle physics experiments with clean, isolated initial states, realistic macroscopic environments are often noisy and dissipative. Recognising the limitations of traditional EFTs has recently sparked intense progress at the interface of high-energy physics and condensed matter. These developments 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, controllable framework for this endeavour. This chapter presents this versatile framework and illustrates how the Schwinger-Keldysh formalism captures the influence of unknown environments, manifesting as dissipation and noise, on observational probes. These notes are based on a series of lectures held during the La Ricotta Summer School "The Disordered Universe 2025" from 21 July to 1 August 2025.

These pedagogical lecture notes address how effective field theory can describe cosmological observables when inaccessible degrees of freedom induce dissipation, noise, and decoherence. They review the Schwinger–Keldysh formalism, develop local open scalar theories, extend the construction to single-clock inflation, and outline issues for electromagnetism and gravity. The framework doubles fields along the forward and backward time contours and organises operators using $\varphi_r=(\varphi_++\varphi_-)/2$ and $\varphi_a=\varphi_+-\varphi_-$. Normalisation, Hermiticity, and influence-functional positivity impose $S[\varphi_r,0]=0$, $S[\varphi_r,\varphi_a]=-S^*[\varphi_r,-\varphi_a]$, and $\operatorname{Im}S\geq0$. A quadratic example is mapped through a Hubbard–Stratonovich transformation to Langevin dynamics with damping $\gamma$ and noise covariance $2\beta\delta(x-y)$. Propagators and perturbative diagrammatics are derived explicitly. Flat-space contact bispectra exhibit total-energy and folded-channel denominators shifted by $3i\gamma/2$, illustrating how dissipation regularises folded enhancements. For inflation, local operators are constructed from the surviving diagonal symmetries, with the mean Goldstone field transforming nonlinearly and the difference field linearly. The construction relates linear dissipation to cubic interactions and identifies no additional independent background tadpole in the class considered. Gauge-theory and gravitational extensions emphasise preserving both contour copies of gauge redundancy despite energy or charge exchange with the environment. The local description assumes environmental correlation lengths and times much shorter than Hubble scales and neglects environmental backreaction. Models producing environmental excitations near horizon crossing fall outside this approximation. Non-equilibrium power counting, cutoff structure, and systematic gravitational EFTs on time-dependent backgrounds remain open issues.