Negative energy density

There are some universe models where $Lambda < 0$. In this case, the energy density of the dark-energy becomes negative. At this point, does it make sense to talk about "negative dark energy density"? Or is it possible to think of this energy as curvature on space-time? Such that, $Lambda < 0$ will imply a negative curvature and $Lambda > 0$ positive one.

For instance if we have a only matter with $Omega_m = 0.3$ the universe will have negative curvature with $Omega_{kappa} = 0.7$.

When we add positive dark energy such that $Omega_{Lambda} = 0.7$ we would have $Omega_{kappa} = 0$.

If we add negative dark energy such that $Omega_{Lambda} = -0.7$, we would have $Omega_{kappa} = 1.4$

So adding positive energy density increases the curvature.

In other words is there a something call "negative" energy density ? or
Does all negative energy densities are thought in terms of the curvature effects on space-time?