[Paper Review] $S_8$ Tension in the Context of Dark Matter-Baryon Scattering

Adam He, Mikhail M. Ivanov+2 more|arXiv (Cornell University)|Jan 19, 2023

Dark Matter and Cosmic Phenomena53 references4 citations

TL;DR

This paper proposes a dark matter-baryon scattering model where 10% of sub-GeV dark matter undergoes velocity-independent elastic scattering with baryons, suppressing small-scale structure. Using BOSS full-shape galaxy clustering data and an $S_8$ prior from DES, the model shows a $\sim 3\sigma$ preference for a non-zero scattering cross-section, reducing $S_8$ tension and suppressing linear power by $\sim 20\%$ at $k \lesssim 1~h/\mathrm{Mpc}$, consistent with small-scale structure constraints.

ABSTRACT

We explore an interacting dark matter (IDM) model that allows for a fraction of dark matter (DM) to undergo velocity-independent scattering with baryons. In this scenario, structure on small scales is suppressed relative to the cold DM scenario. Using the effective field theory of large-scale structure, we perform the first systematic analysis of BOSS full-shape galaxy clustering data for the IDM scenario, and we find that this model alleviates the $S_8$ tension between large-scale structure and Planck data. Adding the $S_8$ prior from DES to our analysis further leads to a mild $\sim3σ$ preference for a non-vanishing DM-baryon scattering cross-section, assuming $\sim 10\%$ of DM is interacting and has a particle mass of 1 MeV. This result produces a modest $\sim 20$% suppression of the linear power at $k\lesssim 1~h$/Mpc, consistent with other small-scale structure observations. Similar scale-dependent power suppression was previously shown to have the potential to resolve $S_8$ tension between cosmological data sets. The validity of the specific IDM model explored here will be critically tested with upcoming galaxy surveys at the interaction level needed to alleviate the $S_8$ tension.

Motivation & Objective

• To investigate whether dark matter-baryon scattering can alleviate the $S_8$ tension between early- and late-universe measurements.
• To constrain the dark matter-baryon scattering cross-section using BOSS full-shape galaxy clustering data for the first time in an interacting dark matter (IDM) framework.
• To test whether scale-dependent suppression of the linear matter power spectrum from IDM can reconcile $S_8$ values from Planck CMB and DES weak lensing data.
• To assess robustness of the IDM model against prior choices and consistency with Milky Way satellite and Lyman-$\alpha$ forest constraints.

Proposed method

• The study employs an effective field theory of large-scale structure to model the impact of dark matter-baryon scattering on the matter power spectrum, introducing a scale-dependent transfer function suppression.
• It performs a systematic cosmological analysis using the full-shape clustering of galaxies from the Baryon Oscillation Spectroscopic Survey (BOSS), incorporating non-linear corrections to the power spectrum.
• The model assumes a fraction $f_\chi = 10\%$ of dark matter scatters elastically with baryons via a velocity-independent cross-section $\sigma_0$, with dark matter masses ranging from 100 keV to 100 MeV.
• The analysis combines BOSS data with Planck CMB and DES $S_8$ priors, using $\chi^2$ minimization to compare the IDM model against $\Lambda$CDM.
• It tests prior robustness by applying a log-uniform prior on $\sigma_0$ over $[-30, -23]$, ensuring results are not biased by prior choice.
• Marginalized posterior distributions for cosmological parameters are computed and visualized to assess constraints and model preference.

Experimental results

Research questions

• RQ1 Can a dark matter-baryon scattering model with a 10% interacting fraction reduce the $S_8$ tension between Planck CMB and DES weak lensing data?
• RQ2 Does the inclusion of BOSS full-shape galaxy clustering data provide a statistically significant preference for a non-zero dark matter-baryon scattering cross-section?
• RQ3 To what extent does the IDM model suppress the linear matter power spectrum at small scales, and is this consistent with existing Lyman-$\alpha$ forest and Milky Way satellite constraints?
• RQ4 How robust is the preference for the IDM model to changes in the prior on the scattering cross-section?

Key findings

• The IDM model with $f_\chi = 10\%$ and $m_\chi = 1~\mathrm{MeV}$ shows a $\sim 3\sigma$ preference for a non-zero dark matter-baryon scattering cross-section when combining BOSS and DES $S_8$ data.
• The model reduces the $S_8$ tension by suppressing the linear matter power spectrum by $\sim 20\%$ at $k \lesssim 1~h/\mathrm{Mpc}$, consistent with small-scale structure observations.
• The $\Delta\chi^2_{\mathrm{min}}$ for the Planck + BOSS + DES combination is $-6.7$ for $m_\chi = 1~\mathrm{MeV}$, $f_\chi = 10\%$, indicating a significant improvement over $\Lambda$CDM.
• Even under a log-uniform prior on $\sigma_0$, the model achieves $\Delta\chi^2_{\mathrm{min}} = -5.6$, confirming robustness and a $>2\sigma$ preference over $\Lambda$CDM.
• The model's suppression profile matches the plateau-like form inferred from joint lensing and CMB data, supporting its potential to resolve $S_8$ tension.
• The results are consistent with constraints from the Milky Way satellite population and the Lyman-$\alpha$ forest, which limit power suppression to $\lesssim 25\%$ in the $0.2 \lesssim k \lesssim 2~h/\mathrm{Mpc}$ range.