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.
