The pseudo-complex FLRW model and the time evolution of the Hubble parameter

Abstract The pseudo-complex version of the Friedmann–Lemaître–Robertson–Walker model (pcFLRW) is presented within the framework of pseudo-complex General Relativity (pcGR). In this approach, dark energy emerges as a geometric consequence of the pseudo-complex structure, leading to a specific functional form for the Hubble parameter H (z) characterized by a single geometric parameter β. This parameter governs the effective dark-energy equation of state via p_ = - _ p Λ = - β ε Λ and is directly linked to the present-day time derivative of the Hubble parameter through Ḣ₀ = 32 (-1) H₀² H ˙ 0 = 3 2 (β - 1) H 0 2. Using recent DESI BAO data, we constrain = 1. 0426 0. 0144 β = 1. 0426 ± 0. 0144, which yields a positive Ḣ₀ (0. 94 0. 32) 10^-17\, (km/s²) /Mpc H ˙ 0 ≃ (0. 94 ± 0. 32) × 10 - 17 (km / s 2) / Mpc. This contrasts with the Λ CDM prediction, where Ḣ₀ H ˙ 0 is negative (Ḣ₀ -0. 45 H₀² H ˙ 0 ≈ - 0. 45 H 0 2 for standard parameters), indicating that in pcGR the expansion rate is increasing with time while in Λ CDM it decreases. The best-fit value also implies a deceleration parameter q = -0. 9361 0. 0216 q =