Beyond delta: Tailoring marked statistics to reveal modified gravity
Models that seek to explain cosmic acceleration through modifications to General Relativity (GR) evade stringent Solar System constraints through a restoring, screening mechanism. Down-weighting the high density, screened regions in favor of the low density, unscreened ones offers the potential to enhance the amount of information carried in such modified gravity models. In this work, we assess the performance of a new "marked" transformation and perform a systematic comparison with the clipping and logarithmic transformations, in the context of $\Lambda$CDM and the symmetron and $f(R)$ modified gravity models. Performance is measured in terms of the fractional boost in the Fisher information and the signal-to-noise ratio (SNR) for these models relative to the statistics derived from the standard density distribution. We find that all three statistics provide improved Fisher boosts over the basic density statistics. The model parameters for the "marked" and clipped transformation that best enhance signals and the Fisher boosts are determined. We also show that the mark is useful both as a Fourier and real space transformation; a marked correlation function also enhances the SNR relative to the standard correlation function, and can on mildly non-linear scales show a significant difference between the $\Lambda$CDM and the modified gravity models. Our results demonstrate how a series of simple analytical transformations could dramatically increase the predicted information extracted on deviations from GR, from large-scale surveys, and give the prospect for a potential detection much more feasible.