Open Effective Field Theory and the Physics of Cosmological Collider Signals

Abstract

We examine the origin of the cosmological collider signal using the framework of open effective field theories. Focusing on the single exchange of a massive scalar field, we demonstrate that the trispectrum splits cleanly into its local and non-local components once the heavy-field propagators are decomposed in the Keldysh basis. Integrating out the massive degree of freedom yields a single-field effective field theory for the light scalar that necessarily contains both unitary operators and non-unitary contributions associated with dissipation and stochastic noise. We show that the leading local signal in parity-preserving theories arises from the unitary part of this effective field theory, whereas the non-local signal is intrinsically associated with its stochastic sector. The effective field theory coefficients themselves are a priori non-analytic in the external kinematics; however, this non-analyticity can be softened when a scale hierarchy - such as the heavy-mass expansion - is imposed, up to spurious contributions that ultimately cancel in observables. Finally, we establish a connection between the cosmological collider signal and entropy production, linking the observable non-local signal to intrinsic properties of the quantum state, including its degree of mixedness.

Figures (5)

• Figure 1: The open single-field EFT interpolates between a closed multi-field EFT where cosmological collider physics is conventional studied and a closed single-field EFT where the heavy fields are completely integrated out. Here $M_p$ denotes Planck scale, $\Lambda$ denotes the cutoff of the closed multi-field EFT and $m_\sigma$ denotes collectively the mass of the heavy fields $\sigma$. At an energy scale $H<E<m_\sigma$, the open single-field EFT is insufficient to explicitly resolve on-shell heavy particle states, but it does capture the stochastic disturbances due to a noisy environment of heavy fields.
• Figure 2: Illustration of the progression from a two-field microphysical model (Left) to a single-field time-local open EFT (Right). The trispectrum $\mathcal{I}$ is conveniently decomposed in the Keldysh basis into three contributions, each with a distinct physical origin. Integrating out the $\sigma$ field initially yields a non-local open EFT (Middle), which incorporates dissipation, governed by the Pauli-Jordan propagator $G^\Delta_\sigma$, and noise, governed by the Keldysh propagator $G^K_\sigma$. At a given order in perturbation theory, one can employ the free equations of motion to recast this EFT in a time-local form. This procedure introduces non-analyticities in the EFT coefficients; however, in the presence of a suitable hierarchy of scales, these non-analyticities are systematically removed through a perturbative expansion in the hierarchy parameter.
• Figure 3: An open perspective of cosmological collider signals. Assuming parity invariance, the leading local signals along with the infinite tower of contact EFT operators map to unitary effects in the single-field open EFT. The subleading local signals, on the other hand, manifest themselves as dissipation whereas the non-local signals appear as stochastic noise. Here $\mathcal{E}$ denotes the heavy-field environment and the arrows denote the momentum flow.
• Figure 4: 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 5: In-in diagrammatics of the $-+$ diagram $\mathcal{I}_{-+}$ (Left) and its incidence on the computation of linear purity $S_2$ (Right). One obtain the latter from the former by closing the momenta loops.