An Analytically Tractable Marked Power Spectrum

TL;DR

This paper develops an analytical framework for the marked power spectrum in cosmology, demonstrating its potential to extract non-Gaussian information efficiently and matching simulations with minimal uncertainties.

Contribution

It introduces a low-order polynomial mark for the marked power spectrum, enabling analytical predictions that align with N-body simulations and discusses degeneracies and future applications.

Findings

Analytical results match N-body simulations for matter and biased tracers.

A low-order polynomial mark controls theoretical uncertainties effectively.

Degeneracies can be broken using auto- and cross-spectra with the unmarked field.

Abstract

The increasing precision of cosmology data in the modern era is calling for methods to allow the extraction of non-Gaussian information using tools beyond two-point statistics. The marked power spectrum has the potential to extract beyond two-point information in a computationally efficient way while using much of the infrastructure already available for the power-spectrum. In this work we explore the marked power spectrum from an analytical perspective. In particular, we explore a low-order polynomial for the mark that allows us to better control the theoretical uncertainties and we show that with minimal new degrees of freedom the analytical results match measurements from N-body simulations for both the matter field and biased tracers in redshift space. Finally, we show that even within the limited forms of mark that we consider, there are degeneracies that can be broken by inclusion of the marked auto-spectrum or the cross-spectrum with the unmarked field. We discuss future theoretical developments that would enable us to apply this approach to survey data.