Sufficient observables for large scale structure in galaxy surveys

Understand

Beyond the linear regime, the power spectrum and higher order moments of the matter field no longer capture all cosmological information encoded in density fluctuations.

• While non-linear transforms have been proposed to extract this information lost to traditional methods, up to now, the way to generalize these techniques to discrete processes was unclear; ad hoc extensions had some success.
• We pointed out in Carron and Szapudi (2013) that the logarithmic transform approximates extremely well the optimal "sufficient statistics", observables that extract all information from the (continuous) matter field.
• Building on these results, we generalize optimal transforms to discrete galaxy fields.