GFT condensate cosmology as an open system: ordinary matter as a dephasing environment and the emergent Newton coupling

We extend the single-mode group field theory (GFT) condensate cosmology of Calcinari, Greco, Oriti and Pellecchia (CGOP), in which quartic and sextic interactions generate dustlike and cosmological-constant terms in the emergent relational Friedmann equation, by coupling the condensate to ordinary matter treated as an environment with an explicit Gorini–Kossakowski–Sudarshan–Lindblad (GKSL) generator, Markovian in relational time. For an environment that records the volume (Lindblad operator ∝ Nˆ ) the dissipator leaves the whole distribution of the number of quanta untouched and damps the coherences, among them the squeezing correlation that drives the expansion. In the free theory the late-time relational expansion rate is then exactly r+ = (Γd^2 + 4ω^2)^1/2 − Γd; read as CGOP read the closed theory, this is the law Geff/G = ((1 + εd^2)^1/2 − εd)^2 with εd = Γd/2ω, which amounts to a redefinition of G unless the bare coupling is fixed independently. An environment that records the field (L ∝ Xˆ ) leaves the rate unchanged: the sign of the effect is fixed by the operator. With interactions, the free moment hierarchy of the volume-recording environment closes exactly at every degree, so that the interaction-generated terms can be computed at first order in the couplings without any closure and at any εd: their equations of state are shifted, exactly, to w4=−2εd^2+4εd^3− . . . for the dust-like term and w6=−1−6εd^2+24εd^3−. . . for the Λ-like term, by the statistical mixing of the dephased state. The Gaussian closure used in the closed model fails at first order once dephasing is present. For every environment that couples to the volume, with or without memory, the expansion efficiency obeys an exact ceiling, so that Geff ≤ G wherever a late-time rate exists. The environment also favours the lowest spin among several modes unless the frequencies grow with the spin, and it broadens the distribution of the volume, by a factor of order one through a bounce. A diluting environment gives Geff a history with a calculable lag; since the single-mode model contains no radiation era, comparisons with nucleosynthesis and lunar laser ranging bound the translation between relational and cosmic time rather than the model. Expected outcomes were written down before each computation, and those not met as written are reported (App. I); the verification protocol, including the use of AI tools, is described in App. H.