Holographic Origin of the MOND Acceleration Scale and Partial Alleviation of the Hubble Tension in Information Field Theory

We present the gravitational sector of Information Field Theory (IFT), a scalar-tensor framework formulated in the Jordan frame in which a dynamical scalar field Φ of mass dimension one encodes the volumetric entanglement entropy of the quantum vacuum. The action is cast in a dimensionally consistent Brans-Dicke form; an AQUAL-type non-linear kinetic structure yields the deep-MOND interpolation function μ(x) = x/(1+x) and the Baryonic Tully-Fisher relation v⁴ = GMa₀. The MOND acceleration scale a₀ = λ²cH₀/(2π) emerges from a holographic boundary condition at the Hubble horizon fixed by the Ryu–Takayanagi relation. At cosmological scales, applying the first law of thermodynamics (Cai & Kim 2005) to the modified horizon entropy yields a holographic back-reaction εH(z)H₀ in the Friedmann equation. A single-parameter MCMC fit (ε = 0.052 ± 0.007, 68% C.L.) to Planck 2018 + DESI DR1 + SH0ES shifts H₀ by +0.6 km/s/Mpc, partially alleviating but not resolving the Hubble tension. The model is strictly quintessence (w ≥ −1); DESI DR2 (2025) data disfavour the IFT cosmological sector at ≈3σ, while the MOND sector remains unaffected. Falsifiable predictions for Euclid and CSST are outlined. Submitted to Universe (MDPI), June 2026.