An Effective Geometric Contribution to Dark Energy in Hassan-Rosen Bimetric Gravity: Structural Predictions from Exchange Symmetry

We study the cosmology of ghost-free Hassan-Rosen bimetric gravity under the restrictive ansatz beta_n = beta₄₋ₙ, which we refer to as the discrete exchange symmetry g <-> f. This ansatz coincides, in the case M_g = M_f, with the "symmetric models" introduced by Hassan, Schmidt-May and von Strauss (arXiv:1407.2772; special case alpha = 1 of their condition alpha^(4-n) beta_n = alpha^n beta₄₋ₙ). It defines a predictive three-parameter subclass of bigravity. Whereas Hassan-Schmidt-May-von Strauss investigated the implications of this ansatz for the massive-gravity limit, we explore here its late-time cosmological phenomenology and identify two consequences that we believe to be new in this generality: (i) a universal linear-order CPL constraint w_a = -3(1+w_0) along trajectories converging to the de Sitter attractor at xi -> 1, and (ii) the universality of the linearised eigenvalue lambda = -3H of the FLRW background at xi = 1, independent of the bigravity parameters. These results bear not on the ansatz itself but on the constraints that dust-matter conservation and late-time dynamics impose upon it. We position the analysis explicitly as a late-time effective field theory valid in the post-recombination regime. The framework does not resolve the cosmological-constant problem: it shifts the fine-tuning from a direct adjustment of Lambda to an adjustment of the primordial deviation |xi_CMB - 1| ~ 10^-11. This record contains:- HR_theorem_v1.17.pdf (English manuscript, 22 pages)- HR_theorem_v1.17_FR.pdf (French translation, 15 pages)- HR_theorem_v1.17.tex / HR_theorem_v1.17_FR.tex (LaTeX sources)- B5_basin_scan.py (ancillary: reproduces Appendix E symbolic + numerical scan, seed 42)