$\hat{\mathbf{I}}{\text{c◯}}_1\hat{\mathbf{I}}{\text{c◯}}_2$-$\hat{\mathbf{I}}›$CDM: A promising phenomenological extension of the standard model of cosmology

Abstract

We investigate a phenomenological extension of the standard $\hat{I}›$CDM framework, the $\hat{I}{\text{c◯}}_1\hat{I}{\text{c◯}}_2$-$\hat{I}›$CDM model, in which the total energy density of the universe is expanded in powers of $1+z$. This parameterization recovers $\hat{I}›$CDM and introduces two additional terms, $\hat{I}{\text{c◯}}_1(1+z)$ and $\hat{I}{\text{c◯}}_2(1+z{)}^2$, in the dark energy sector alongside the cosmological constant, leading to a physically interpretable and observationally testable effective dark energy dynamics. Using Planck cosmic microwave background (CMB) data, we find that the model allows additional freedom in the late-time expansion history while preserving standard early-universe physics. When DESI baryon acoustic oscillation (BAO) data are included, the inferred Hubble constant is $H_0=69.74\pm 0.77\mathrm{km}{\mathrm{s}}^{-1}\mathrm{Mp}{\mathrm{c}}^{-1}$ (68% CL), consistent with 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, modifying late-time dynamics while maintaining standard early-time cosmology. Overall, controlled late-time deviations from $\hat{I}›$CDM improve cosmological concordance.

12 pages, 2 figures; Major updates; Matches the version published in Physics of The Dark Universe