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In general relativity, an IDEAL (Intrinsic, Deductive, Explicit, ALgorithmic)characterization of a reference spacetime metric $g_0$ consists of a set oftensorial equations $T[g]=0$, constructed covariantly out of the metric $g$,its Riemann curvature and their derivatives, that are satisfied if and only if$g$ is locally isometric to the reference spacetime metric $g_0$. The samenotion can be extended to also include scalar or tensor fields, where theequations $T[g,\phi]=0$ are allowed to also depend on the extra fields $\phi$.We give the first IDEAL characterization of cosmological FLRW spacetimes, withand without a dynamical scalar (inflaton) field. We restrict our attention towhat we call regular geometries, which uniformly satisfy certain identities orinequalities. They roughly split into the following natural special cases:constant curvature spacetime, Einstein static universe, and flat or curvedspatial slices. We also briefly comment on how the solution of this problem hasimplications, in general relativity and inflation theory, for the constructionof local gauge invariant observables for linear cosmological perturbations andfor stability analysis.

IDEAL characterization of isometry classes of FLRW and inflationary spacetimes