ETHOS - An Effective Theory of Structure Formation: From dark particle physics to the matter distribution of the Universe

TL;DR

ETHOS establishes a practical framework that translates diverse dark matter microphysics into a compact set of effective parameters that govern the linear matter power spectrum and self-interactions. By deriving a Boltzmann-equation-based mapping from DM–DR interactions and DM self-scattering to ETHOS parameters (ωDR, a_n, α_l, and velocity-averaged cross sections), the authors show how to classify and compare broad classes of DM models through their structure-formation signatures. They provide concrete mappings for models with massive mediators, hidden-charged DM, and non-Abelian DR, and illustrate the resulting impact on dark acoustic oscillations and damping in P(k). This framework enables efficient, model-agnostic exploration of DM phenomenology with a public CAMB-based implementation, offering a scalable path to confront a wide range of DM theories with observations. The approach also lays groundwork for extensions to other dark-sector physics, including warm DM analogs, while preserving core insights into how microphysics imprint large-scale structure.

Abstract

We formulate an effective theory of structure formation (ETHOS) that enables cosmological structure formation to be computed in almost any microphysical model of dark matter physics. This framework maps the detailed microphysical theories of particle dark matter interactions into the physical effective parameters that shape the linear matter power spectrum and the self-interaction transfer cross section of non-relativistic dark matter. These are the input to structure formation simulations, which follow the evolution of the cosmological and galactic dark matter distributions. Models with similar effective parameters in ETHOS but with different dark particle physics would nevertheless result in similar dark matter distributions. We present a general method to map an ultraviolet complete or effective field theory of low energy dark matter physics into parameters that affect the linear matter power spectrum and carry out this mapping for several representative particle models. We further propose a simple but useful choice for characterizing the dark matter self-interaction transfer cross section that parametrizes self-scattering in structure formation simulations. Taken together, these effective parameters in ETHOS allow the classification of dark matter theories according to their structure formation properties rather than their intrinsic particle properties, paving the way for future simulations to span the space of viable dark matter physics relevant for structure formation.

Figures (4)

• Figure 1: Left panel: Transfer function $T(k) \equiv P_{\rm ETHOS}(k)/P_{\rm CDM}(k)$ for four different exponents $n$ parametrizing the redshift dependence of the DM drag opacity $\dot{\kappa}_\chi= - (\Omega_{\rm DR}h^2) a_n(4/3)(1+z)^{n+1}/(1+z_{\rm D})^n$. The values of $a_n$ are chosen such that all models have the same DM drag epoch $z_{\rm drag}$, which we define via the criterion $-\dot{\kappa}_\chi(z_{\rm drag}) = \mathcal{H} (z_{\rm drag})$. The actual values used are $\{a_1,a_2,a_3,a_4\} = \{6.56,3.5\times10^{1}, 1.86\times10^{2}, 9.95\times10^{2}\}$ Mpc$^{-1}$. All models assume $\omega_{\rm DR} = 1.35\times10^{-6}$ , $\alpha_l = 1$, and $b_n = 0$. For completeness, we also used $\xi = 0.5$, $m_\chi = 10$ GeV, and $d_n = a_n$, but the results shown above are insensitive to these specific choices. Right panel: Dark matter drag visibility function for the same models as the left panel. The DM drag visibility function is essentially the probability distribution function for the time at which a DM particle last scatter off DR.
• Figure 2: Left panel: Transfer function for three different values of $\alpha_2$ for a model characterized by a nonvanishing value of $a_4$. The model shown here assumes fermionic DR with $a_4 = 2.24\times10^{4}$ Mpc$^{-1}$, $\xi = 0.5$, $m_\chi = 2$ TeV, $\eta _{\rm DR} = \eta_\chi =2$, $b_n = 0$, and $\alpha_{l\geq3}=1$. Right panel: Similar to the left panel but for a model with $a_2 = 3.5\times 10^1$ Mpc$^{-1}$. We assume fermionic DR with $\xi = 0.5$, $m_\chi = 10$ GeV, $\eta _{\rm DR} = \eta_\chi =2$, $b_n = 0$, and $\alpha_{l\geq3}=1$.
• Figure 3: Left panel: Transfer function $T(k) \equiv P_{\rm ETHOS}(k)/P_{\rm CDM}(k)$ for three different values of $\alpha_3$ for a model characterized by a nonvanishing value of $a_4$. The model shown here assumes fermionic DR with $a_4 = 2.24\times10^{4}$ Mpc$^{-1}$, $\xi = 0.5$, $m_\chi = 2$ TeV, $\eta _{\rm DR} = \eta_\chi =2$, $b_n = 0$, $\alpha_2 =1$, and $\alpha_{l\geq4}=1$. Right panel: Similar to the left panel but for a model with $a_2 = 3.5\times 10^1$ Mpc$^{-1}$ and $m_\chi = 10$ GeV.
• Figure 4: Left panel: Velocity dependence of the self-interaction cross section over mass for DM interacting via a Yukawa potential mediated by a messenger particle $\phi$2011PhRvL.106q1302LHooper:2012cwTulin:2012wiTulin:2013teo. The model shown with the thick red solid curve is an example of a symmetric DM model that primarily scatters in the classical regime ($m_\chi v\gg m_\phi$) with a momentum-transfer cross sections given by the average of Eqs. \ref{['sigT-']} and \ref{['sigT+']}. The thin solid blue line is an example of asymmetric DM that primarily scatters in the classical regime with a momentum-transfer cross sections given by Eq. \ref{['sigT+']}. The dashed cyan curve is an example of an asymmetric DM model similar to the model put forward in Ref. Kaplinghat:2015aga. This model primarily scatters in the nonperturbative regime ($m_\chi v\lesssim m_\phi$) and we refer the reader to the Appendix of Ref. Tulin:2013teo for an explicit analytical formula that is valid in this regime. In all cases, the colored points show the average values $\langle \sigma_{T}\rangle_{v_{M}}/m_\chi$ (as defined in Eq. \ref{['eq:ETHOS_vel_ave']}) for the three typical velocity ranges shown here by the gray bands. Note that the width of the gray bands is for illustration purposes only. Right panel: Similar to the left panel but for atomic DM models Goldberg:1986nkKaplan:2009deBehbahani:2010xaKaplan:2011yjCline:2012isCyr-Racine:2013abCline:2013zcaCline:2013pca. Here, the models are labeled by the value of $R$, which is the mass ratio of the two particles forming the dark atom. We show the approximate fitting formula for the momentum-transfer cross section given in Eq. (10) of Ref. Cline:2013pca with a dark fine-structure constant value of $\alpha_D = 0.05$. For all the cases shown, the DM mass is determined from the relation $m_\chi = (R/\alpha_D)^{2/3}$ GeV Cline:2013zca. The colored points show the values of $\langle \sigma_{T}\rangle_{v_{ M}}/m_\chi$ for each typical velocities $v_{M}$.