Supernova constraints on spatial variations of the vacuum energy density

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Abstract
We consider a very simple toy model for a spatially varying “cosmological constant,” where we are inside a spherical bubble (with a given set of cosmological parameters) that is surrounded by a larger region where these parameters are different. This model includes essential features of more realistic scenarios with a minimum number of parameters. We calculate the luminosity distance in the presence of spatial variations of the vacuum energy density using linear perturbation theory and discuss the use of type Ia supernovae to impose constraints on this type of model. We find that presently available observations are only constraining at very low redshifts, but also provide independent confirmation that the high-redshift supernovae data do prefer a relatively large positive cosmological constant.