Cosmological Constant and Universe Evolution in EBIKK-β Gravity: Emergent Dark Energy from Entropic-Kaluza-Klein Theory

This paper presents a novel derivation of the cosmological constant(Λ) within the Entropic-Born-Infeld-Kaluza-Klein (EBIKK-β) framework.Key results include:• Emergent Λ from combined Kaluza-Klein compactification and entropic Tent ln det G terms• Singularity-free early universe with β-regulated curvature• Testable deviations from ΛCDM:– Time-varying effective Λ: |Λ˙ /Λ| ∼ 10−15 yr−1– CMB low-ℓ suppression (∆Cℓ/Cℓ ∼ 10−6)– Modified matter power spectrum turnover at k ∼ β−1/2The model reproduces observed cosmic acceleration while predictingdistinct signatures for next-generation surveys like Euclid and CMB-S4.