Modeling the Marked Spectrum of Matter and Biased Tracers in Real- and Redshift-Space

Abstract

We present the one-loop perturbation theory for the power spectrum of the marked density field of matter and biased tracers in real-and redshift-space. The statistic has been shown to yield impressive constraints on cosmological parameters; to exploit this, we require an accurate and computationally inexpensive theoretical model. Comparison with N -body simulations demonstrates that linear theory fails on all scales, but inclusion of one-loop Effective Field Theory terms gives a substantial improvement, with ∼ 5% accuracy at z = 1. The expansion is less convergent in redshift-space (achieving ∼ 10% accuracy), but there are significant improvements for biased tracers due to the freedom in the bias coefficients. The large-scale theory contains non-negligible contributions from all perturbative orders; we suggest a reorganization of the theory that contains all terms relevant on large-scales, discussing both its explicit form at one-loop and structure at infinite-loop. This motivates a low-k correction term, leading to a model that is sub-percent accurate on large scales, albeit with the inclusion of two (three) free coefficients in real-(redshift-)space. We further consider the effects of massive neutrinos, showing that beyond-EdS corrections to the perturbative kernels are negligible in practice. It remains to see whether the purported gains in cosmological parameters remain valid for biased tracers and can be captured by the theoretical model.

The effective field theory and perturbative analysis for log-density fields

“…Afterwards, we have shown that the large scales are fixed by adding two free parameters (2.59) in both the Taylor-APT and the EoM-APT schemes at tree level. Those free parameters were already considered in the case of the marked fields in [25]. We have shown that the inclusion of those parameters -at least in the log transformation case -not only takes into account the resummation of higher-order terms but also fixes the series' convergence issues described above in the text.…”

“…The series constructed on that way has a better loop-hierarchy and gets closer to the simulation result at low redshift. Afterwards, we show that the inclusion of a few free parameters, already considered in [25], can improve the small k behaviour for both schemes.…”

“…It was shown by [23] that marked fields can improve the constraints in the neutrino mass sum by a factor of 80. An effective field theory for marked fields was constructed by [24,25]. Once A is also more linear and increases the weight of cosmic voids in the correlation functions, we also expect it to provide more stringent constraints on neutrinos, dark energy, and gravity [26][27][28].…”

“…Notice that both the EoM-APT and the Taylor-APT models work equally good at all loop-orders after adding those free terms. As pointed out by [25] for the marked field, the inclusion of those terms can embrace a resummation of all loop-order terms. 10 Here we can see that those terms are not only doing this resummation job but they also parametrize the correct scaling and fix an inherent problem of the perturbative theory for A, namely that it is asymptotic and fails already on the largest scales for A.…”

“…in order to guarantee that the Taylor series does not diverge [25]. In case the condition (2.66) is not satisfied, the free parameters that parametrize scales < R −1 and the counter-terms that parametrize UV scales > k NL will contain mixed information and some extra degeneracies might arise.…”