Interacting Dark Sector and Precision Cosmology

TL;DR

This work extends the Interacting Dark Sector (IDS) model, where a fraction of dark matter interacts with a thermal dark radiation background, to address both the σ8 and H0 tensions. By expanding to a two-component dark matter sector and incorporating LSS data with full k-dependence, the authors show that current large-scale structure measurements increasingly constrain the shape of the matter power spectrum and favor a suppressed clustering scenario induced by IDM-DR interactions. The analysis finds a statistically significant improvement in the global fit relative to ΛCDM (3–4σ) driven largely by Planck SZ data, while the H0 tension remains only mildly alleviated; the work also provides detailed perturbation- and limit-analytic results and highlights the potential of upcoming LSS and 21-cm data to discriminate between WI and DP regimes. Overall, IDS offers a concrete, testable framework for dark-sector physics with observable imprints on the CMB, lensing, and the full MPS.

Abstract

We consider a recently proposed model in which dark matter interacts with a thermal background of dark radiation. Dark radiation consists of relativistic degrees of freedom which allow larger values of the expansion rate of the universe today to be consistent with CMB data ($H_0$-problem). Scattering between dark matter and radiation suppresses the matter power spectrum at small scales and can explain the apparent discrepancies between $Λ$CDM predictions of the matter power spectrum and direct measurements of Large Scale Structure LSS ($σ_8$-problem). We go beyond previous work in two ways: 1. we enlarge the parameter space of our previous model and allow for an arbitrary fraction of the dark matter to be interacting and 2. we update the data sets used in our fits, most importantly we include LSS data with full $k$-dependence to explore the sensitivity of current data to the shape of the matter power spectrum. We find that LSS data prefer models with overall suppressed matter clustering due to dark matter - dark radiation interactions over $Λ$CDM at 3-4 $σ$. However recent weak lensing measurements of the power spectrum are not yet precise enough to clearly distinguish two limits of the model with different predicted shapes for the linear matter power spectrum. In two Appendices we give a derivation of the coupled dark matter and dark radiation perturbation equations from the Boltzmann equation in order to clarify a confusion in the recent literature, and we derive analytic approximations to the solutions of the perturbation equations in the two physically interesting limits of all dark matter weakly interacting or a small fraction of dark matter strongly interacting.

Figures (9)

• Figure 1: Comparison of $\Gamma(a)$ and $H(a)$ for the limits WI and DP. Even though $\Gamma(a) \propto a^{-2}$, the ratio plotted has a changing slope because of the evolving $a$-dependence of $H(a)$. Note that for the DP limit it is sufficient to take $\Gamma_0 \gg H_0$, while for the WI we need $\Gamma \ll H$ during RD. The vertical dashed line is $a_\mathrm{eq}$, the scale factor at matter/radiation equality.
• Figure 2: (Left) Ratio of $\delta_\mathrm{idm}$ in WI to $\delta_\mathrm{cdm}$ in $\Lambda \mathrm{CDM}$. Note that at some point during MD the suppression saturates and remains more or less constant, because $\Gamma \propto a^{-2}$ decays faster than $H \propto a^{-3/2}$. (Right) Ratio of $\delta_\mathrm{cdm}$ and $\delta_\mathrm{idm}$ in DP to $\delta_\mathrm{cdm}$ in $\Lambda \mathrm{CDM}$. Note that after horizon crossing these suppressions are never constant in time. Also, note that $\delta_\mathrm{idm}$ oscillates early on, but later has the same time dependence as $\delta_\mathrm{cdm}$ in DP: the two lines become parallel. The plots were made with CLASS (Blas:2011rf), holding $\boldsymbol{\theta}_{\Lambda \mathrm{CDM}}$ and $\boldsymbol{\theta}_{\mathrm{IDS}}$ fixed.
• Figure 3: CLASS plots of the ratio of the linear MPS from the IDS model to that from $\Lambda \mathrm{CDM}+\Delta N_{\mathrm{fluid}}$ (left) in the WI limit, for different $\Gamma_0$; and (right) in the DP limit, for different $f$. Note the $k$ (in)dependence of the suppression in the left (right) plots.
• Figure 4: CLASS plots of the ratio of the CMB lensing spectrum from the IDS model to that from $\Lambda \mathrm{CDM}+\Delta N_{\mathrm{fluid}}$ (left) in the WI limit, for different $\Gamma_0$; and (right) in the DP limit, for different $f$.
• Figure 5: CLASS plots of the ratio of perturbations $\delta_\mathrm{dm}(\eta)$ and $\psi(\eta)$ from the WI model with $\Gamma_0 = 6\times 10^{-7} \mathrm{Mpc}^{-1}$ to that from the $\Lambda$CDM+$\Delta N_\mathrm{fluid}$ model, both with $\Delta N_\mathrm{fluid}=0.4$, for several wavenumbers $k$ relevant for the first CMB peaks. The vertical lines show the conformal time at radiation/matter equality and at recombination, and the maximum value of $\eta$ corresponds to the conformal time today.