Four-derivative corrections to the neutral-scalar Christodoulou threshold in charged de Sitter black holes

Abstract We study leading parity-even four-derivative corrections to the linear Christodoulou regularity criterion for a neutral, massless, minimally coupled spectator scalar in four-dimensional charged de Sitter black holes. We derive the corrected static solution, cold extremality relation, near-horizon geometry, Cauchy-horizon surface gravity, and neutral scalar quasinormal spectrum within Einstein-Maxwell effective theory. Near cold extremality, the scalar equation reduces analytically to the finite-temperature anti-de Sitter two-dimensional throat problem. We find that the dominant nonstationary spherically symmetric mode retains its cold-limit regularity ratio through first order, while higher angular sectors respond to the deformation of the relative throat radii. The finite-distance neutral-scalar Christodoulou boundary nevertheless shifts because the relevant exterior scalar spectrum and the unequal horizon surface gravities enter the regularity ratio. At smaller and intermediate cosmological scales, positive effective coefficients move the Christodoulou threshold to larger normalized separation of the Cauchy and event horizons. Toward the larger cosmological-scale part of the cold branch, the same coefficient directions move that threshold back toward the cold endpoint. The reversal accompanies a transition in the quasinormal family that supplies the spectral gap. We further show that the coefficient combination governing the fixed-charge extremal mass parameter differs generically from those governing the cold throat and the finite-distance neutral-scalar boundary. Extremality therefore does not determine a universal direction for the neutral-scalar Christodoulou-threshold correction. Our results identify cosmological scale and spectral-family competition as essential elements in relating effective gravity, black-hole extremality, and Cauchy-horizon regularity in this spectator sector.