Kinematic Reconstruction of $Λ(t)$CDM Models

TL;DR

The paper investigates Λ(t)CDM by reconstructing two linear-in-redshift quantities, $\Lambda(z)=\Lambda_0+\Lambda_1 z$ and $Q(z)=Q_0+Q_1 z$, (plus a constant-$Q$ case) using a Bayesian framework on Cosmic Chronometers, Pantheon+SH0ES, and BAO data. The $\Lambda(z)$ model yields a closed-form $H(z)$ depending on $\Omega_m$ and $\Omega_{\Lambda1}$, while the $Q(z)$ model requires solving a nonlinear ODE for $E(z)=H/H_0$ numerically; both approaches test for deviations from standard $\Lambda$CDM. The results show weak constraints: $\Omega_{\Lambda1}=0.02\pm0.14$, $\mathcal{Q}_0=0.1\pm5.8$, $\mathcal{Q}_1=0.06\pm0.67$, and $\mathcal{Q}_0=-0.1\pm5.7$ (for the constant case) at 68% c.l., with constraints consistent with $\Lambda$CDM but leaving room for modest Λ variation. Overall, current data favor $\Lambda$CDM, though large margins remain for new physics; future analyses including Planck CMB data and non-parametric reconstructions could tighten these bounds and provide model-independent tests of vacuum decay.

Abstract

In this work, we have performed two kinematic parametrizations for $Λ(t)$CDM models, namely, the linear expansions $Λ(z)=Λ_0+Λ_1z$ and $Q(z)=Q_0+Q_1z$, where $Q$ is the interaction term. In the case of the $Q(z)$ parametrization, we have also tested the particular case of a constant interaction term, $Q(z)=Q_0$. In order to constrain the free parameters of these models, we have used Cosmic Chronometers (CC), SNe Ia data (Pantheon+\&SH0ES) and BAO data. As a general result, we have found weak constrains over the free parameters of the analysed models. In the case of $Λ(z)$, we have found for the $Λ$ variation parameter, $Ω_{\Lambda1}\equiv\frac{Λ_1}{3H_0^2}=0.02\pm0.14$. In the case of the $Q(z)$ parametrization, we have worked with the dimensionless interaction term $\gQ(z)\equiv\frac{8πGQ(z)}{3H_0^3}$, from which we have found $\gQ_0=0.1\pm5.8$ and $\gQ_1=0.06\pm0.67$. In the particular case of a constant interaction term, we have found $\gQ_0=-0.1\pm5.7$. All these constraints are at 68\% c.l. The constraints we have obtained are compatible with the standard $Λ$CDM model, although still providing a large margin for $Λ$ variation.

Figures (7)

• Figure 1: Triangle plot of cosmological parameters for the $\Lambda(z)$ model. Marginal distributions and confidence contours for the parameters $M$, $H_0$, $\Omega_m$, and $\Omega_{\Lambda1}$ in the model with a time-varying cosmological constant $\Lambda(z) = \Lambda_0 + \Lambda_1 z$. The colors indicate different data combinations: gray (CC+BAO), red (CC+Pantheon+&SH0ES), and blue (CC+BAO+Pantheon+&SH0ES).
• Figure 2: Joint analysis of the cosmological parameters for the $\Lambda(z)$ model. Marginal distributions and confidence contours for the parameters $M$, $H_0$, $\Omega_m$, and $\Omega_{\Lambda1}$ in the model with a time-varying cosmological constant $\Lambda(z) = \Lambda_0 + \Lambda_1 z$. CC+BAO+Pantheon+SH0ES.
• Figure 3: Triangle plot of cosmological parameters for the interacting model $Q(z) = Q_0 + Q_1 z$ for different data combinations. Marginal distributions and confidence contours for the parameters $M$, $H_0$, $\Omega_m$, $\mathcal{Q}_0$, and $\mathcal{Q}_1$ in the model with a redshift-dependent interaction between dark matter and dark energy.
• Figure 4: Triangle plot of the joint analysis of the cosmological parameters for the interacting model $Q(z) = Q_0 + Q_1 z$. Marginal distributions and confidence contours for the parameters $M$, $H_0$, $\Omega_m$, $\mathcal{Q}_0$, and $\mathcal{Q}_1$ in the model with a redshift-dependent interaction between dark matter and dark energy.
• Figure 5: Triangle plot of different data combinations for the interacting model with constant $Q_0$. Marginal distributions and confidence contours for the parameters $M$, $H_0$, $\Omega_m$, and $\mathcal{Q}_0$ in the model with a constant interaction between dark matter and dark energy.