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We explore the effect of applying a non-linear transformation to theLyman-$\alpha$ forest transmitted flux $F=e^{-\tau}$ and the ability ofanalytic models to predict the resulting clustering amplitude. Both thelarge-scale bias of the transformed field (signal) and the amplitude of smallscale fluctuations (noise) can be arbitrarily modified, but we were unable tofind a transformation that increases significantly the signal-to-noise ratio onlarge scales using Taylor expansion up to third order. In particular, however,we achieve a 33% improvement in signal to noise for Gaussianized field intransverse direction. On the other hand, we explore an analytic model for thelarge-scale biasing of the Ly$\alpha$ forest, and present an extension of thismodel to describe the biasing of the transformed fields. Using hydrodynamicsimulations we show that the model works best to describe the biasing withrespect to velocity gradients, but is less successful in predicting the biasingwith respect to large-scale density fluctuations, especially for very nonlineartransformations.

Optimizing BAO measurements with non-linear transformations of Lyman-alpha forest