Toward a Unified String-EFT Resolution to the H0 and S8 Tensions

Early Dark Energy (EDE) is a leading phenomenological resolution to the Hubble (H₀) tension, yet standard models typically rely on ad-hoc scalar potentials. We propose a theoretical framework for transient EDE pulses emerging from the D²ᵏR⁴ higher-derivative tower in Type IIB string theory. By localizing these operators on D7-brane stacks within a warped Large Volume Scenario (LVS), we derive quantized potential slopes α(k) via explicit dimensional reduction. We show that the modular weight of Cold Dark Matter (CDM) determines a matter coupling β = -1/(2√2) ≈ -0.354, a value topologically locked by the D7-brane embedding. We provide a 2-field stability analysis suggesting that the EDE pulse remains approximately decoupled from the volume stabilization. This framework provides a mechanism that may reconcile the sound horizon shift with matter growth suppression, potentially alleviating the clustering tension typical of axion-like EDE.