A negative cosmological constant in the dark sector

We consider the possibility that the dark sector of our universe contains a negative cosmological constant dubbed $\lambda$. For such models to be viable, the dark sector should contain an additional component responsible for the late-time accelerated expansion rate ($X$). We explore the departure of the expansion history of these models from the concordance \lcdm model. For a large class of our models the accelerated expansion is transient with a nontrivial dependence on the model parameters. All models with $w_X>-1$ will eventually contract and we derive an analytical expression for the scale factor $a(t)$ in the neighbourhood of its maximal value. We find also the scale factor for models ending in a Big Rip in the regime where dustlike matter density is negligible compared to $\lambda$. We address further the viability of such models, in particular when a high $H_0$ is taken into account. While we find no decisive evidence for a nonzero $\lambda$, the best models are obtained with a phantom behaviour on redshifts $z\gtrsim 1$ with a higher evidence for nonzero $\lambda$. An observed value for $h$ substantially higher than $0.70$ would be a decisive test of their viability.