What does the Marked Power Spectrum Measure? Insights from Perturbation
  Theory
  The marked power spectrum is capable of placing far tighter constraints on
cosmological parameters (particularly the neutrino mass) than the conventional
power spectrum. What new information does it contain beyond conventional
statistics? Through the development of a perturbative model, we find that the
mark induces a significant coupling between non-Gaussianities, which are
usually found on small scales, and large scales, leading to the additional
information content. The model is derived in the context of one-loop
perturbation theory and validated by comparison to $N$-body simulations across
a variety of mark parameters. At moderate redshifts, including for massive
neutrino cosmologies, the theory is in good agreement with the simulations. The
importance of non-linear gravitational effects on the large-scale spectra
complicates the modeling as there is no well-defined convergence radius of the
theory at low $z$. Extension to higher perturbative order and biased tracers is
possible via a similar approach, and a simple model of the latter is shown to
yield promising results. The theory becomes non-perturbative at redshift zero
for small smoothing scales, with important contributions from higher-order
terms: these will need to be studied before the full power of this tool can be
realized.
