The Breathing Universe: 711_Future Causal Reachability in a Horizon-Regulated Cosmology

Abstract

The future causal accessibility of an expanding universe is determined by the remaining future conformal interval rather than by the instantaneous Hubble radius. In a spatially flat Friedmann-Lemaitre-Robertson-Walker spacetime, the maximum remaining comoving null distance is chi_future(t) = c integral_t^t_f [dt'/a(t')]. A finite value defines a future cosmological event horizon. The corresponding proper radius, R_e(t) = a(t) chi_future(t), may remain finite, diverge, or vanish without changing this primary causal classification. This work develops a homogeneous event-horizon-regulated realization of the Breathing Universe Model (BUM) and uses it to formulate future causal reachability as a globally constrained cosmological problem. A dynamical vacuum-tension variable H_vac is coupled to an effective horizon-regulated vacuum contribution, Lambda_BUM = xi(H_vac)/R_e^2, while the cosmological expansion rate H_c = dot(a)/a is kept explicitly distinct from H_vac. The event horizon satisfies the local equation dot(R_e) = H_c R_e - c, but this equation alone does not select the physical event horizon. The required solution additionally satisfies the global future condition lim[t -> t_f] R_e(t)/a(t) = 0. The resulting cosmology is therefore naturally formulated as a nonlinear boundary-value problem. General asymptotic criteria are derived for finite and divergent future conformal intervals. For a(t) proportional to t^p, a finite event horizon exists for p > 1, while the critical p = 1 case requires logarithmic refinement. De Sitter-like, stretched-exponential, super-exponential, and finite-terminal futures are also classified. A central result is that R_e -> infinity does not imply event-horizon removal: horizon existence is determined by convergence of the future conformal integral. The globally selected BUM solution is compared with a matched flat LambdaCDM reference using the same H_0, Omega_m0, and Omega_r0. Small expansion-history differences determine both past observable-distance shifts and future event-horizon shifts, but through different integration domains. For identical fixed photon or constant-peculiar-speed spacecraft protocols, Delta_M = Delta_R, so a finite fractional event-horizon shift maps directly into the same fractional change in idealized comoving causal reach. A genuine finite-to-horizon-free transition instead requires nonperturbative asymptotic classification. The framework establishes a single falsifiable chain from vacuum-tension dynamics through cosmological expansion and global horizon selection to future causal accessibility. The same parameter set and the same globally selected branch must account for past observables and determine the future horizon without retuning.