Translation and Rotation Equivariant Normalizing Flow (TRENF) for Optimal Cosmological Analysis*

In this talk we introduce Translation and Rotation Equivariant Normalizing Flow (TRENF), a generative Normalizing Flow (NF) model which explicitly incorporates translation and rotation symmetries. We apply TRENF to cosmological data analysis, where TRENF allows direct access to the high dimensional data likelihood p(x|y) as a function of the labels y, such as cosmological parameters. In contrast to traditional analyses based on summary statistics, the NF approach has no loss of information since it preserves the full dimensionality of the data. On Gaussian random fields, the TRENF likelihood agrees well with the analytical expression and saturates the Fisher information content in the labels y. On nonlinear cosmological overdensity fields from N-body simulations, TRENF leads to significant improvements in constraining power over the standard power spectrum summary statistic.