A First‑Principles Derivation of the Cosmological Constant and the Hubble Constant within the Framework of the First‑Principle Unified Theory of Light Strings ——Also on the Inevitability of the Big Bang

Within the framework of the First‑Principle Unified Theory of Light Strings, this paper rigorously demonstrates that the Big Bang is not an assumption but a logical necessity of the theory. Starting from the initial kinetic energy of light strings, the conditions for particle formation, the speed‑of‑light limit, and the mechanism of cosmic expansion, we deduce that the universe originated from a hot, dense state and expands linearly and isotropically at the speed of light. Based on this linear expansion model, we derive the simple relation between the Hubble constant and the age of the universe: $H_0^{\text{th}} = 1/t_0$. Furthermore, by combining with the dynamics of the light‑string field, we obtain the cosmological constant $\Lambda = H_0^2/c^2 = 1/(c^2 t_0^2) = 1/R^2$, where $R = c t_0$ is the radius of the universe. We also distinguish the theoretical intrinsic Hubble constant from the observed apparent values, thereby resolving the Hubble tension without invoking dark energy. All cosmological parameters are derived from first principles, achieving a fully closed logical chain from cosmic origin to expansion and constants.