Information-Constrained Scalar-Tensor Theory (ICST)

ABSTRACTGeneral Relativity, despite its macroscopic success, breaks downmathematically in singularity regimes. We present theInformation-Constrained Scalar-Tensor Theory (ICST), which integrates localinformation density as a dimensionless scalar field C into gravitationaldynamics. The theory is proven ghost-free via DHOST Class Ia mapping(Langlois & Noui 2016), possessing 3 physical degrees of freedom (2 tensor +1 scalar). The GW170817 constraint (|c_T - c| < 10^-15) is naturally satisfiedvia Vainshtein screening. The critical threshold C_crit = (1/2) ln(E^2 / 4 ln 2)≈ 1.1578 is analytically derived from the self-consistent solution of theBekenstein minimum area bound and the disformal Jacobian degeneracycondition. The dimensionless system constant E ≈ 5.3 is determined from auniversal geometric principle: E* = 1/sqrt(H_0^2 l_P^2 Omega_Lambda) ≈5.30, requiring no fine-tuning beyond Planck 2018 measurements. The EuclidMission (2026-2028) prediction ΔP/P ≈ 1.8% at k ≈ 0.15 h/Mpc is detectableat ≥ 3σ. The Page curve is restored at t_Page^ICST ≈ 0.67 t_Page^Schwarzvia a disformal negative feedback mechanism. In Kerr geometry, theergosphere produces enhanced C field values, with early echo signaturespotentially detectable by LISA.Keywords: Scalar-tensor theory, DHOST, Bekenstein-Hawking bound, informationparadox, Vainshtein screening, Euclid Mission, Page curve, Kerr geometry, phasetransition