Gravitational Waves in a Noisy Room express

Original: "Homogeneous and Isotropic Linearized Gravity as a Caldeira--Leggett System"

arXiv:2607.28209v1 · 2026-07-30 · CC BY 4.0 · 1 min

Weak perturbations of spacetime can be described as a system interacting with matter, like a pendulum pushed by passersby.

A pendulum in a noisy room is constantly jostled by people passing by. Its motion is a mix of regular swings and random jerks. Something similar happens with weak gravitational waves against the backdrop of an expanding universe. In Einstein's general relativity, these waves are tiny ripples in spacetime. But they are not isolated. They are surrounded by matter, which acts like a crowd in the room.

The Caldeira–Leggett model was originally developed for quantum dissipation — for instance, an electron losing energy in a crystal. Now it has been applied to gravity itself.

Physicists have found that the equations for such waves in an expanding universe (the one described by Friedmann) match those of open systems. This is the famous Caldeira–Leggett model. When the “reservoir” of matter is integrated out, what remains is a generalized Langevin equation for the metric perturbation (the quantity describing curvature). All the information about the environment collapses into a single quantity — the spectral density. It shows how strongly matter rattles at different frequencies. This adds a stochastic component — random jolts.

The spectral density is the environment’s ID card: it shows how matter at each frequency acts on the wave, much like a graph of noise volume in a room for different pitches.

The new approach turns gravitational waves into a quantum open system. They are no longer treated as isolated. Interactions with matter can be accounted for. One can even move to a quantum description. Thus the pendulum-universe, jostled by matter, begins to reveal its quantum nature.

Original abstract

as written by the authors arXiv:2607.28209v1

We establish the equivalence between homogeneous and isotropic linearized gravity with minimally coupled degrees of freedom and the Caldeira--Leggett model of open systems. This connects gravitation to an established system-plus-reservoir formalism, which we use throughout. Eliminating the reservoir reduces the equations of linearized gravity to a generalized Langevin equation for the metric perturbation, with the environmental influence condensed in the spectral density. The equivalence also yields a natural setting for reduced quantization of the perturbation and stochastic gravitational dynamics. We analyze the resulting dynamics with Laplace methods, extending results presented in other open-system settings.

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The Caldeira–Leggett model was proposed in 1983 to explain quantum tunneling with dissipation. It became a standard tool in open-system physics and now helps us understand how gravity is quantized.

\ddot{h} + \gamma \dot{h} + \omega^2 h = \eta(t)

Generalized Langevin equation for a gravitational wave: h — metric perturbation, γ — damping coefficient, ω — frequency, η(t) — random force from the environment.

Scientists

Albert Einstein Barry Barish Kip Thorne Richard Feynman Russell Hulse Edward Witten

Concepts

equivalence principle teleparallel gravity geodesic equation cosmological homogeneity quantum gravity equivalence principle test newtonian limit law of conservation of momentum Friedmann equations flat space scalar charge Noether's theorem general relativity Wheeler-DeWitt equation equipartition theorem lagrangian supergravity fq gravity classical gravity gravitational theory

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Gravitational Waves in a Noisy Room express

Original abstract