Counting propagating degrees of freedom in open gravitational dynamics

Develop a general prescription to count the propagating degrees of freedom in the open effective field theory of gravity constructed via the Schwinger–Keldysh formalism, in which the dynamics involves the metric g_{μν}, the advanced metric a^{μν}, and dissipative operators such as M_{μν}(g_{μν}, g^{00}, K_{μν}, ∇_μ; t).

Background

The paper formulates an open effective field theory (EFT) for gravity in the Schwinger–Keldysh framework to describe metric dynamics coupled to an unknown environment (the dark sector). In this setting, the field content includes both the physical metric and an advanced (inverse) metric, and the action contains dissipative operators.

While linear-order phenomenology is explored, the authors note foundational issues that are not yet settled. Among these is a systematic method to count the number of propagating degrees of freedom when dissipation and doubled fields are present—a nontrivial task compared to standard closed EFTs.

References

A few foundational aspects are still under investigation, including a prescription to count propagating degrees of freedom, additional consistency conditions on dissipative operators , and the non-linear realization of gauge symmetries . In this work, we set aside these interesting open questions and instead concentrate on a minimal model, whose internal consistency has been established in .

— Phenomenology of an Open Effective Field Theory of Dark Energy  (2603.12321 - Salcedo et al., 12 Mar 2026) in Open Effective Field Theories paragraph (main text)