Kinematic Reconstruction of $\Lambda(t)$CDM Models

In this work, we have \textbf{analysed} two kinematic parametrizations for $\Lambda(t)$CDM models, namely, the linear expansions $\Lambda(z)=\Lambda_0+\Lambda_1z$ 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 constraints over the free parameters of the analysed models. In the case of $\Lambda(z)$, we have found for the $\Lambda$ variation parameter, $\Omega_{\Lambda1}\equiv\frac{\Lambda_1}{3H_0^2}=0.02\pm0.14$. In the case of the $Q(z)$ parametrization, we have worked with the dimensionless interaction term $\gQ(z)\equiv\frac{8\pi GQ(z)}{3H_0^3}$, from which we have found $\gQ_0 = 2.2 \pm 2.7$ and $\gQ_1 = -6.2 \pm 7.6$. In the particular case of a constant interaction term, we have found $\gQ_0 = 0.18 \pm 0.7$. All these constraints are at 68\% c.l. The constraints we have obtained are compatible with the standard $\Lambda$CDM model, although still providing a large margin for $\Lambda$ variation.