CMB constraints on spatial variations of the vacuum energy density

In a recent article, a simple `spherical bubbleʹ toy model for a spatially varying vacuum energy density was introduced, and type Ia supernovae data was used to constrain it. Here we generalize the model to allow for the fact that we may not necessarily be at the center of a region with a given set of cosmological parameters, and discuss the constraints on these models coming from cosmic microwave background radiation data. We find tight constraints on possible spatial variations of the vacuum energy density for any significant deviations from the center of the bubble and we comment on the relevance of our results.