On the question of measuring spatial curvature in an inhomogeneous
  universe
  The curvature of a spacetime, either in a topological sense, or averaged over
super-horizon-sized patches, is often equated with the global curvature term
that appears in Friedmann's equation. In general, however, the Universe is
inhomogeneous, and gravity is a nonlinear theory, thus any curvature
perturbations violate the assumptions of the FLRW model; it is not necessarily
true that local curvature, averaged over patches of constant-time surfaces,
will reproduce the observational effects of global symmetry. Further, the
curvature of a constant-time hypersurface is not an observable quantity, and
can only be inferred indirectly. Here, we examine the behavior of curvature
modes on hypersurfaces of an inhomogeneous spacetime non-perturbatively in a
numerical relativistic setting, and how this curvature corresponds with that
inferred by observers. We also note the point at which observations become
sensitive to the impact of curvature sourced by inhomogeneities on inferred
average properties, finding general agreement with past literature.
