What does the Marked Power Spectrum Measure? Insights from Perturbation Theory

Abstract: 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.