Finite FLRW Spacetimes, Causal Boundaries, and the Origin of Λ

We investigate the variational boundary-value problem for a finite Friedmann–Lemaître–Robertson–Walker (FLRW) spacetime globally completed by an exterior Schwarzschild vacuum. To construct the solution, we introduce a spherical hypersurface Σ separating an FLRW interior M₋ from an exterior region M₊ and treat it as an internal junction of the composite spacetime M = M₋ ∪ Σ ∪ M₊. Continuity of the induced metric and extrinsic curvature provides a sufficient condition for stationarity of the joined gravitational action. The local cosmological geometry can remain the ordinary FLRW solution throughout the interior; what changes is its global completion. Instead of continuing the homogeneous FLRW spacetime indefinitely beyond its asymptotic cosmological horizon, the finite interior is completed by a Schwarzschild exterior across a common null horizon, R_Λ− = r_s. This yields a black-hole spacetime with an FLRW cosmological interior and a finite global completion. Different interior observers possess different, generally overlapping, observer-centred causal patches of the same homogeneous finite geometry. Each measures the same apparent-horizon scale, which asymptotically approaches R_Λ− = rs, while no observer encounters a material edge or preferred centre. The cosmological constant thereby admits an interpretation as a quantity selected by the global causal completion rather than as an independent local bulk parameter. Within this framework the infinite-FLRWlimit, r_s → ∞, implies Λ₋ → 0. Since the observed cosmological constant is non-zero, this infinite limit is incompatible with the observed late-time acceleration: the measured value of Λ₋ instead selects a finite gravitational scale. Thus a causal interpretation of the observed FLRWgeometry naturally points to a finite global completion. This difference can have profound consequences for the cosmological interpretation.