buchert_backreaction_zero
plain-language theorem explainer
The declaration shows that the Buchert backreaction scalar vanishes identically under the ILG source modification. Cosmologists testing source-side kernels against distances and growth would cite it to attribute late-time anomalies to weighting rather than metric variance. The proof reduces directly to reflexivity on the definition that fixes the scalar at zero for irrotational flow.
Claim. The Buchert backreaction scalar $Q_D$, which measures the variance of the expansion rate over a spatial domain, equals zero in the ILG model.
background
The Buchert backreaction scalar $Q_D$ quantifies the variance of the expansion rate across a spatial domain $D$. For a potential-flow velocity field the scalar vanishes identically, as recorded in the definition of the ILG backreaction scalar. The ILG framework modifies only the source term while leaving the metric and expansion rate unchanged, so the velocity field remains irrotational and the scalar is zero.
proof idea
The proof is a one-line reflexivity reduction that matches the definition of the ILG backreaction scalar, which is fixed at zero by the potential-flow property of the velocity field.
why it matters
This theorem supplies the zero backreaction component required by the backreaction certificate theorem, which also incorporates X-reciprocity and PPN safety bounds. It confirms a core result in the Buchert backreaction section: ILG produces zero backreaction because it is a source modification rather than a metric one. The result aligns with the Recognition Science emphasis on potential-flow properties in the gravity domain.
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