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An Open System Approach to Gravity

Santiago Agüí Salcedo, Thomas Colas, Lennard Dufner, Enrico Pajer

Abstract

Several major open problems in cosmology, including the nature of inflation, dark matter, and dark energy, share a common structure: they involve spacetime-filling media with unknown microphysics, and can be probed so far only through their gravitational effects. This observation motivates a systematic open-system approach to cosmology, in which gravity evolves in the presence of a generic, unobservable environment. In this work, we develop a general framework for open gravitational dynamics based on general relativity and the Schwinger-Keldysh formalism, carefully addressing the nontrivial constraints imposed by diffeomorphism invariance. At the quantum level, our path integral formulation computes the gravitational density matrix in perturbation theory around a semi-classical spacetime. As illustrative applications, we study inflation and the propagation of gravitational waves in classical regimes where environmental interactions are non-negligible. In the inflationary context, our framework reproduces the known Open Effective Field Theory of Inflation in the decoupling limit and extends it to include gravitational interactions. For gravitational waves, we derive the most general conservative and dissipative corrections to propagation. Remarkably, we find that the leading-order gravitational birefringence is dissipative in nature, whereas conservative birefringence appears only at higher derivative order, opposite to the electromagnetic case. Our results pave the way to modeling dissipative effects in the late universe.

An Open System Approach to Gravity

Abstract

Several major open problems in cosmology, including the nature of inflation, dark matter, and dark energy, share a common structure: they involve spacetime-filling media with unknown microphysics, and can be probed so far only through their gravitational effects. This observation motivates a systematic open-system approach to cosmology, in which gravity evolves in the presence of a generic, unobservable environment. In this work, we develop a general framework for open gravitational dynamics based on general relativity and the Schwinger-Keldysh formalism, carefully addressing the nontrivial constraints imposed by diffeomorphism invariance. At the quantum level, our path integral formulation computes the gravitational density matrix in perturbation theory around a semi-classical spacetime. As illustrative applications, we study inflation and the propagation of gravitational waves in classical regimes where environmental interactions are non-negligible. In the inflationary context, our framework reproduces the known Open Effective Field Theory of Inflation in the decoupling limit and extends it to include gravitational interactions. For gravitational waves, we derive the most general conservative and dissipative corrections to propagation. Remarkably, we find that the leading-order gravitational birefringence is dissipative in nature, whereas conservative birefringence appears only at higher derivative order, opposite to the electromagnetic case. Our results pave the way to modeling dissipative effects in the late universe.

Paper Structure

This paper contains 83 sections, 392 equations, 3 figures, 1 table.

Table of Contents

  1. Introduction
  2. The medium: particle physics, cosmology and condensed matter.
  3. Unknown microphysics.
  4. Gravitational observables.
  5. An open effective field theory for gravity.
  6. Outline.
  7. Reader's guide.
  8. Notation and conventions.
  9. Summary of the main results
  10. A heuristic approach to open gravity.
  11. The symmetry story.
  12. Open gravity.
  13. The general propagation of gravitational waves.
  14. The decoupling limit.
  15. Learnings from open electromagnetism
  16. ...and 68 more sections

Figures (3)

  • Figure 1: Some distinctions between particle physics, cosmology and condensed matter. Left: Particle physics studies particles and their interactions atop a of clean and isolated vacuum. Middle: Cosmology reconstructs the properties of the universe by analyzing perturbations that propagate through an unknown medium to our detectors. Right: Condensed matter creates and probes engineered media, which can be observed externally and under controlled conditions.
  • Figure 2: Illustration of the closed-time-path, where time is running from left to right in both contours and the arrow represent path ordering (time ordering in $\ket{\Omega}$ and anti-time-ordering in $\bra{\Omega}$). Memory of the initial conditions is quickly lost due to dissipation.
  • Figure 3: The tensor-to-scalar ratio $r$ as a function of $\Gamma_T/H$, for different choices of $\beta_{6,0}$. The observational constraint $r < 0.036$BICEPKeck:2024stm restricts the allowed region of parameters. Ongoing and future surveys, such as SO SimonsObservatory:2018koc, CMB S4 CMB-S4:2020lpa and LiteBIRD LiteBIRD:2022cnt will put tighter constraint on this parameter.