$\mathbf{Ω_1Ω_2}$-$\mathbfΛ$CDM: A promising phenomenological extension of the standard model of cosmology
Suresh Kumar
TL;DR
The paper introduces an $\Omega_1\Omega_2$--$\Lambda$CDM extension by expanding the total energy density in powers of $ (1+z) $, yielding an effective dark-energy density $\rho_{ m de}(z)=\rho_{ m crit,0}[\Omega_\Lambda+\Omega_1(1+z)+\Omega_2(1+z)^2]$ and a dark-energy EOS $w_{\rm de}(z)=-1+\frac{1}{3}\frac{\Omega_1(1+z)+2\Omega_2(1+z)^2}{\Omega_\Lambda+\Omega_1(1+z)+\Omega_2(1+z)^2}$, which allows phantom-divide crossing and a de Sitter attractor as $z\to -1$. The authors fit Planck 2018 CMB data and DESI BAO using CLASS and MontePython with flat priors on $\Omega_1$ and $\Omega_2$, finding Planck-alone degeneracies that are broken by DESI, yielding $H_0=69.74\pm0.77$ km s$^{-1}$ Mpc$^{-1}$ and $\Omega_1=-0.112^{+0.063}_{-0.048}$, $\Omega_2\sim 10^{-2}$ for Planck+DESI. The reconstructed $w_{\rm de}(z)$ features a quintessence-like regime at high $z$, a phantom crossing near $z\approx 4.6$, a minimum $w_{\rm de}\approx -1.09$ at $z\approx 2.14$, and an eventual approach to $-1$, enhancing late-time acceleration and alleviating the $H_0$ tension while preserving early-universe physics. Overall, the framework demonstrates that modest late-time deviations from $\Lambda$CDM can improve cosmological concordance and motivates further perturbation analyses and broader data tests.
Abstract
We investigate a phenomenological extension of the standard $Λ$CDM framework, the $Ω_1Ω_2$-$Λ$CDM model, in which the total energy density of the universe is expanded in powers of $1+z$. This parameterization recovers the standard $Λ$CDM framework and contributes two additional terms, $Ω_1(1+z)$ and $Ω_2(1+z)^2$, in the dark energy sector, alongside the cosmological constant, leading to a physically interpretable and observationally testable dynamics of effective dark energy. Using Planck cosmic microwave background (CMB) data, we find that the model allows increased freedom in the late-time expansion history while preserving the standard early-universe physics. When DESI baryon acoustic oscillation (BAO) data are included in the analysis, the inferred Hubble constant is $H_0 = 69.74 \pm 0.77~\mathrm{km\,s^{-1}\,Mpc^{-1}}$ (68\% CL), which is consistent with recent Tip of the Red Giant Branch (TRGB) measurements from the Carnegie--Chicago Hubble Program (CCHP). The reconstructed dark energy equation of state exhibits a smooth transition across the phantom divide followed by asymptotic de Sitter behavior, leading to modified late-time dynamics of universe while maintaining standard early-time cosmology. Overall, our results demonstrate that controlled late-time deviations from $Λ$CDM can improve cosmological concordance.