The BAHAMAS project: evaluating the accuracy of the halo model in predicting the non-linear matter power spectrum

Abstract

The halo model formalism is widely adopted in cosmological studies for predicting the growth of large-scale structure in the Universe. However, to date there have been relatively few direct comparisons of the halo model with more accurate (but much more computationally expensive) cosmological simulations. We test the accuracy of the halo model in reproducing the non-linear matter power spectrum, P(k), when the main inputs of the halo model (specifically the matter density profiles, halo mass function, and linear bias) are taken directly from the BAHAMAS simulations and we assess how well the halo model reproduces P(k) from the same simulations. We show that the halo model generally reproduces P(k) in the deep non-linear regime (1-halo) to typically a few percent accuracy, but struggles to reproduce (approx. 15 per cent error) P(k) at intermediate scales of $0.1 \lesssim k \ [h/{\rm Mpc}] \lesssim 3$ at z = 0, marking the transition between the 1-halo and 2-halo terms. We show that the magnitude of this error is a strong function of the halo mass definition (through its effects on radial extent of haloes) and of redshift. Furthermore, we test the accuracy of the halo model in recovering the relative impact of baryons on P(k). We show that the systematic errors in recovering the absolute P(k) largely cancel when considering the relative impact of baryons. This suggests that the halo model can make precise predictions for the baryonic suppression, offering a fast and accurate way to adjust collisionless matter power spectra for the presence of baryons and associated processes.

Improved analytical modeling of the non-linear power spectrum in modified gravity cosmologies

“…We also note that in this work, we focus on modeling only the dark matter PS. At our scales of interest (k between 0.1−2.5 h/ Mpc), PS is not significantly influenced by baryons, as baryonic suppression in PS is of the order of a few percent for k < 1 − 5 h/ Mpc [117][118][119]. However, [105,108,117] have shown that HM provides the flexibility, which allows it to add additional parameters that can incorporate baryonic effects from hydrodynamical simulation.…”

“…At our scales of interest (k between 0.1−2.5 h/ Mpc), PS is not significantly influenced by baryons, as baryonic suppression in PS is of the order of a few percent for k < 1 − 5 h/ Mpc [117][118][119]. However, [105,108,117] have shown that HM provides the flexibility, which allows it to add additional parameters that can incorporate baryonic effects from hydrodynamical simulation. Accounting for such effects in our MG PS modeling is a significant endeavor, and is well beyond the scope of this work.…”

Tomography-based observational measurements of the halo mass function via the submillimeter magnification bias

“…Lastly, it should be noted that the halo model used in this work has its shortcomings and appears not to show the accuracy required for very precise measurements regarding cosmology, mainly due to the transition between the 1-halo and 2-halo regimes and/or baryonic physics (Mead et al 2015;Mead, A. J. et al 2020;Philcox et al 2020;Acuto et al 2021). Future work will also address the possible improvements that could arise when the model is refined.…”

Tomography-based observational measurements of the halo mass function via the submillimeter magnification bias

“…Another possibility could of course be the use of other HMF models derived from alternatives to the standard excursion set formalism, like the stochastic theory by Lapi & Danese (2020. Lastly, it should be noted that the halo model used in this work has its shortcomings and appears not to show the accuracy required for very precise measurements regarding cosmology, mainly due to the transition between the 1-halo and 2halo regimes and/or baryonic physics (Mead et al 2015(Mead et al , 2020Philcox et al 2020;Acuto et al 2021). Future work will also…”