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We show that the dynamics of the Higgs field during inflation is not affectedby metric fluctuations if the Higgs is an energetically subdominant lightspectator. For Standard Model parameters we find that couplings between Higgsand metric fluctuations are suppressed by $\mathcal{O}(10^{-7})$. They arenegligible compared to both pure Higgs terms in the effective potential and theunavoidable non-minimal Higgs coupling to background scalar curvature. Thequestion of the electroweak vacuum instability during high energy scaleinflation can therefore be studied consistently using the Jordan frame actionin a Friedmann--Lema\^itre--Robertson--Walker metric, where the Higgs-curvaturecoupling enters as an effective mass contribution. Similar results apply forother light spectator scalar fields during inflation.

Do metric fluctuations affect the Higgs dynamics during inflation?