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

Recent advances in gravitational dressing and quantum reference frames have shown that the
algebra of observables associated with horizons acquires a Type~II structure, permitting a
well-defined notion of generalized entropy.  These works characterize the entropy associated with horizons but do not address how an
observer should assign expectation values to local energy–momentum observables ---
the quantities that enter the semiclassical Einstein equation.

In this paper we develop the Relativity of Reconstruction (RoR), a framework for defining
observer-dependent effective stress tensors in spacetimes with horizons.  We construct a
class $\mathcal{M}_{\mathrm{holo}}$ of admissible coarse-graining maps $F_q$, characterized by
positivity, static-patch covariance, a single geometric scale $\ell_q\sim H^{-1}$, and a
thermodynamically fixed modular contribution.  For any $F_q\in\mathcal{M}_{\mathrm{holo}}$, we
prove a universality theorem: the geometric contribution to $\langle F_q T_{\mu\nu}\rangle$
scales as $H^4$ independently of kernel shape, UV field content, or interactions, while the
modular term contributes a universal $H^2 M_{\mathrm{Pl}}^2$ piece fixed by de~Sitter
thermodynamics.  The resulting observer-dependent effective stress tensor takes the form
\[
\langle T_{\mu\nu}(q)\rangle
=-(C_1 H^4 + C_2 H^2 M_{\mathrm{Pl}}^2) g_{\mu\nu},
\]
with $F_q\to\mathrm{id}$ and $T_{\mu\nu}(q)\to T_{\mu\nu}$ in the flat-space limit.

We then show that the family $\{T_{\mu\nu}(q)\}$ defines a $(G,X)$-structure on the space of
observers, with transition maps determined by the coordinates of $F_q$ within
$\mathcal{M}_{\mathrm{holo}}$.  This global ``observer atlas'' encodes the obstruction to any
observer-independent notion of vacuum energy and provides the operator backbone for an
observer-relative semiclassical Einstein equation developed in future work.