Dynamical dark energy in models with evolution close to $Λ$CDM

TL;DR

The paper investigates whether kinematic proximity to ΛCDM, encoded by $j(z)\approx1$, guarantees dynamical proximity $w_{\rm DE}(z)\approx-1$ in flat cosmologies. It shows this equivalence is fragile and constructs two analytic almost-ΛCDM models with a small deviation parameter $\epsilon$, deriving explicit $H(z)$, $q(z)$, $\Omega_m(z)$, and $w_{\rm DE}(z)$ to compare with ΛCDM. Although one can adjust present-day cosmographic values to force $w_{\rm DE}(0)=-1$, the models exhibit notable dynamical differences at other redshifts, effectively aligning with a unified dark fluid rather than ΛCDM. DESI constraints further indicate cosmographies that depart from ΛCDM, underscoring the nonrobustness of inferring ΛCDM dynamics from cosmographic data alone.

Abstract

In this communication we address whether or not there is an equivalence between the kinematical and dynamical descriptions of the spatially flat $Λ$CDM model. We address this by investigating whether an almost $Λ$CDM expansion history ($j(z)\approx1$) corresponds to an almost $Λ$CDM model ($w_{\rm DE}(z)\approx-1$) by considering two particular explicit examples. At least for the cases considered, this turns out not to be the case. Instead, what we find is that an almost $Λ$CDM cosmic evolution rather corresponds to an \emph{almost unified dark fluid model}. Considering that one never gets the exact condition $j(z)=1$ from any cosmographic data sets, this raises further questions on whether the $Λ$CDM model is the best candidate for the standard model of the evolution of the universe.

Figures (7)

• Figure 1: Evolution of different kinematic quantities for the almost $\Lambda$CDM evolutionary model-I (left panels) and model-II (right panel). In the last row, we also show the plots of the quantity $H_0 D_L$ for the two evolutionary models, where $D_L=(1+z)\int_0^z \frac{dz}{H(z)}$ is the luminosity distance.
• Figure 2: Evolution of different densities and the density abundance parameters for the almost $\Lambda$CDM evolutionary model-I (left panels) and model-II (right panel).
• Figure 3: Evolution of the dark energy equation of state parameter for the almost $\Lambda$CDM evolutionary model-I (left panels) and model-II (right panel).
• Figure 4: Evolution of the dark energy equation of state in the $w-w'$ plane for the almost $\Lambda$CDM evolutionary model-I (left panels) and model-II (right panel). Here $w_{\rm DE}'\equiv=\frac{dw_{\rm DE}}{d\log(a)}=-(1+z)\frac{dw_{\rm DE}}{dz}$. For both the models, $\{w_{\rm DE}(0),w'_{\rm DE}(0)\}=\{-1,-0.0305144\}$, i.e. they coincide with the $\Lambda$CDM model $w_{\rm DE}=-1$ at $z=0$.
• Figure 5: Evolution of the dark energy equation of state parameter for the almost $\Lambda$CDM evolutionary model-I (left panels) and model-II (right panel).