Cosmological Information in the Marked Power Spectrum of the Galaxy Field

Abstract

Marked power spectra are two-point statistics of a marked field obtained by weighting each location with a function that depends on the local density around that point. We consider marked power spectra of the galaxy field in redshift space that up-weight low-density regions, and we perform a Fisher matrix analysis to assess the information content of this type of statistics using the Molino mock catalogs built on the Quijote simulations. We identify four different ways to up-weight the galaxy field, and we compare the Fisher information contained in their marked power spectra to that of the standard galaxy power spectrum, when considering the monopole and quadrupole of each statistic. Our results show that each of the four marked power spectra can tighten the standard power spectrum constraints on the cosmological parameters Ω m , Ω b , h, n s , and M ν by 15%–25% and on σ 8 by a factor of 2. The same analysis performed by combining the standard and four marked power spectra shows a substantial improvement compared to the power spectrum constraints that is equal to a factor of 6 for σ 8 and a factor of 2.5–3 for the other parameters. Our constraints may be conservative, since the galaxy number density in the Molino catalogs is much lower than the ones in future galaxy surveys, which will allow them to probe lower-density regions of the large-scale structure.

Probing massive neutrinos with the Minkowski functionals of the galaxy distribution

“…We note the combination of the MFs and power spectrum only slightly improves the M ν constraint from the MFs alone, by 2% (from 0.059 to 0.058 eV). This finding is consistent with other works based on the Molino mock catalogs: for the bispectrum monopole [46], marked power spectrum [47], and skew spectra [74], when combined with the power spectrum, the M ν constraint from the statistics alone is improved by 3%, 9%, and 8%, respectively. This may indicate the M ν constraint is dominated by information from higher order statistics.…”

“…For the HOD parameters, the confidence contours rotate notably and expand quickly with the increase of R G . This is because HOD parameters mainly influence structure on small scales [47], as explained above. This strong scale dependence of parameter degeneracies and constraints can also be explained from the perspective of the characteristic scale dependence of the derivatives w.r.t.…”

“…Using the Molino mock galaxy catalogs [46], we obtain accurate simulation-based modeling of the MFs down to mildly nonlinear scales for the redshift-space galaxy distribution and reliable Fisher matrix forecasts with a large number of samples. We also make a direct comparison with other statistics that have been applied to these mock catalogs, such as the power spectrum, the bispectrum monopole [46], and the marked power spectrum [47]. Notably, we detailedly compare the MFs and the power spectrum on parameter degeneracies present in each statistic and parameter constraints from each statistic.…”

“…These step sizes were chosen to make the derivatives for the power spectrum and the bispectrum converged [46]. And they have also been tested to give convergent derivatives for the marked power spectrum [47]. Hence we anticipate the derivatives of the MFs w.r.t.…”

“…The size of each bin is 2π/L, where L = 1h −1 Gpc is the size of the simulation box. We take the same choice of k max as previous works that used the Molino catalogs for Fisher matrix forecasts [46,47,73,74], hence the constraints from the power spectrum may serve as a benchmark for the comparison of the MFs with other statistics.…”