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Field-level inference is emerging as a promising technique for optimallyextracting information from cosmological datasets. Indeed, previous analyseshave shown field-based inference produces tighter parameter constraints thanpower spectrum analyses. However, estimates of the detailed quantitative gainin constraining power differ. Here, we demonstrate the gain in constrainingpower depends on the parameter space being constrained. As a specific example,we find that field-based analysis of an LSST Y1-like mock data set onlymarginally improves constraints relative to a 2-point function analysis in$\Lambda$CDM, yet it more than doubles the constraining power of the data inthe context of $w$CDM models. This effect reconciles some, but not all, of thediscrepant results found in the literature. Our results demonstrate theimportance of using a full systematics model when quantifying the informationgain for realistic field-level analyses of future data sets.

Map-based cosmology inference with weak lensing -- information content and its dependence on the parameter space