Endowing $\mathbf{\Lambda}$ with a dynamic nature: constraints in a spatially curved Universe

In this study, we consider three dark energy models in which $\Lambda$ is not constant, but has a dynamic nature that depends on the Hubble parameter $H$ and/or its time derivative $\dot{H}$. We analyse the generalized running vacuum model, characterized by $\Lambda(H)=A+BH^2+C\dot{H}$, along with the two-parameter models obtained by setting $B$ or $C$ equal to zero. In the case with $C=0$, one gets the classical running vacuum model. Our main aim is to investigate the effects of spatial curvature on the values that the parameters $B$ and/or $C$ are allowed to take. Constraints are obtained via an MCMC analysis, using data from Type-Ia supernovae, baryon acoustic oscillations and the cosmic microwave background, as well as Hubble parameter measurements at different redshifts. Our results indicate that the presence of spatial curvature shifts the characteristic parameter ($B$ or $C$) of each two-parameter running vacuum model away from the null value that constitutes the $\Lambda$CDM limit. Furthermore, in the non-flat scenarios, the introduction of a measurement of the Hubble constant from the high end of the observationally-established range alters the inferred constraints significantly, and in such a way that the two-parameter models deviate from $\Lambda$CDM and are compatible with an open Universe at more than $1\sigma$. We find that the data we use is not sufficient to break the degeneracy between the generalized running vacuum model parameters $B$ and $C$ unless a flat space-time is assumed.