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

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 β . This parameter governs the effective dark-energy equation of state via p_Λ = -β ε _Λ p Λ = - β ε Λ and is directly linked to the present-day time derivative of the Hubble parameter through Ḣ₀ = 3/2(β -1)H₀² H ˙ 0 = 3 2 ( β - 1 ) H 0 2 . Using recent DESI BAO data, we constrain β = 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 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 Λ CDM it decreases. The best-fit value also implies a deceleration parameter q = -0.9361 ± 0.0216 q =