Cosmological Implications of the Information-Loss Framework: Deriving the Observable Universe Horizon Radius

In our previous work (Paper I), we proposed a dimensional-emergence scaling factor (α∼10−2) to bridge the gap between the holographic information capacity (10122 bits) and the vacuum energy density. In this paper, we explore the cosmological implications of this framework. By incorporating the information-loss cut-off α into the Friedmann equations for a flat Friedmann-Lemaître-Robertson-Walker (FLRW) universe, we derive the effective dark energy density. Under the assumption of the Hubble horizon approximation (R=c/H), the theoretical derivation yields an observable universe horizon radius of approximately 4.4×1026 meters. Remarkably, this purely theoretical result converges with the standard ΛCDM model's observation of approximately 46.5 billion light-years. This phenomenological alignment strongly supports the hypothesis that the "vacuum catastrophe" is mathematically equivalent to an information-processing overhead during the emergence of three-dimensional spacetime, providing a novel information-theoretic perspective on the cosmic scale.