Relativity of Reconstruction: Observer–Dependent Vacuum Energy in de Sitter Space

We show that FRW symmetry enforces a Ward identity that trivializes observer-dependent vacuum reconstruction. Under the assumptions of FRW symmetry, state-only reconstruction maps, and overlap consistency, the cocycle class encoding observer-relative holonomy projects to the trivial class in the observable quotient $H^1(M,G/G_{\mathrm{FRW}})$, where $M$ is the spacetime manifold, $G$ the reconstruction gauge group, and $G_{\mathrm{FRW}}$ its FRW-invariant subgroup. This is a structural result about the entire class of state-only observer-relative reconstructions, and implies that FRW-accessible observables are necessarily insensitive to observer-dependent vacuum structure. The empirical success of $\Lambda$CDM in homogeneous cosmology is therefore not accidental but enforced by the symmetry of the observable sector.

To establish and contextualize this result we develop the \emph{Relativity of Reconstruction} (RoR), a framework in which gravitationally relevant stress--energy is reconstructed from observer-restricted operator algebras in the presence of horizons. Vacuum energy is treated as an observer-relative quantity rather than a global scalar. The reconstruction map $F_q$ is canonically realized as the trace-preserving conditional expectation onto the observer algebra in the type~II$_1$ dressed static-patch algebra of Chandrasekaran--Longo--Penington--Witten. Observer reconstructions assemble into a global $(G,X)$ structure with cocycle and holonomy data, and we exhibit explicit nontrivial holonomy in the de~Sitter two-patch system via the modular sign flip across antipodal horizons.

Within this framework we show that Weinberg's cosmological-constant no-go theorem corresponds precisely to the state-only global-section sector of RoR and is therefore recovered rather than evaded. Observable deviations from standard cosmology can arise only in history-dependent channels that violate the FRW Ward identity. We identify the integrated Sachs--Wolfe effect and a growth--lensing consistency relation as natural examples and discuss possible connections to current observational tensions.

The framework yields a sharp empirical criterion: FRW-accessible observables are structurally blind to observer-relative holonomy, whereas a detected deviation in a genuinely history-dependent observable that cannot be absorbed into FRW parameter redefinitions would falsify the state-only sector of the theory, reframing the cosmological constant problem as a structural mismatch between global state properties and observer-relative reconstruction.