Cosmological Constraints on $\Lambda$(t)CDM Models

Problems with the concordance cosmology $\Lambda$CDM as the cosmological constant problem, coincidence problems and Hubble tension has led to many proposed alternatives, as the $\Lambda(t)$CDM, where the now called $\Lambda$ cosmological term is allowed to vary due to an interaction with pressureless matter. Here, we analyze one class of these proposals, namely, $\Lambda=\alpha'a^{-2}+\beta H^2+\lambda_*$, based on dimensional arguments. Using SNe Ia, cosmic chronometers data plus constraints on $H_0$ from SH0ES and Planck satellite, we constrain the free parameters of this class of models. By using the Planck prior over $H_0$, we conclude that the $\lambda_*$ term can not be discarded by this analysis, thereby disfavouring models only with the time-variable terms. The SH0ES prior over $H_0$ has an weak evidence in this direction. The subclasses of models with $\alpha'=0$ and with $\beta=0$ can not be discarded by this analysis. Finally, by using distance priors from CMB, the $\Lambda$ time-dependence was quite restricted.