Probing elastic interactions in the dark sector and the role of $S_8$

TL;DR

This work investigates elastic, momentum-exchanging interactions between dark energy and dark matter, focusing on two covariant realizations: velocity-entrainment with a dark-radiation component and covariant Thomson-like scattering with a constant coupling. They demonstrate that additional radiation can ease the H0 tension while momentum exchange suppresses structure growth to help with the σ8 tension; using Planck2018, BAO, SN Ia, SZ cluster counts, and S8 priors, they find Planck-era data alone place upper bounds on the couplings, but including low-redshift S8 data can hint at nonzero interactions and shift σ8 downward without severely compromising H0. The results suggest a potential universal momentum exchange signal in the dark sector, though a simultaneous, robust resolution of both tensions remains challenging and requires further non-linear and joint-probe analyses. Overall, elastic dark-sector interactions emerge as a promising, minimal extension to ΛCDM that can modestly improve key cosmological tensions under certain data combinations.

Abstract

We place observational constraints on two models within a class of scenarios featuring an elastic interaction between dark energy and dark matter that only produces momentum exchange up to first order in cosmological perturbations. The first one corresponds to a perfect-fluid model of the dark components with an explicit interacting Lagrangian, where dark energy acts as a dark radiation at early times and behaves as a cosmological constant at late times. The second one is a dynamical dark energy model with a dark radiation component, where the momentum exchange covariantly modifies the conservation equations in the dark sector. Using Cosmic Microwave Background (CMB), Baryon Acoustic Oscillations (BAO), and Supernovae type Ia (SnIa) data, we show that the Hubble tension can be alleviated due to the additional radiation, while the $σ_8$ tension present in the $Λ$-Cold-Dark-Matter model can be eased by the weaker galaxy clustering that occurs in these interacting models. Furthermore, we show that, while CMB+BAO+SnIa data put only upper bounds on the coupling strength, adding low-redshift data in the form of a constraint on the parameter $S_8$ strongly favours nonvanishing values of the interaction parameters. Our findings are in line with other results in the literature that could signal a universal trend of the momentum exchange among the dark sector.

Figures (11)

• Figure 1: Evolution of the CDM and DE density contrasts and velocity potentials in the $b$CDM and $\alpha$CDM models for different values of the parameters and wavenumbers. We can see how the growth of the CDM density contrast slows down at late times in both models, thus yielding a suppression in the growth of structures with respect to $\Lambda$CDM.
• Figure 2: Temperature and polarisation CMB angular power spectra for the $\Lambda$CDM and $b$CDM models with $\Omega_{\rm DR}=10^{-5}$ and several values of the interaction parameter $b$. We also show the normalised values defined as $\bar{C}^{xx}_\ell= C^{xx}_{\ell\ b{\rm CDM}}/C^{xx}_{\ell\ \Lambda {\rm CDM}}$, except $\bar{C}^{\rm TE}_\ell$ normalised with the temperature angular power spectrum.
• Figure 3: Temperature and polarisation CMB angular power spectra in $\alpha$CDM for different values of the interacting parameter $\alpha$ and with $N_{\rm eff}=4.046$. The fiducial $w$CDM model with $w=-0.98$ is recovered for $\alpha=0$ and $N_{\rm eff}=3.046$. Normalised differences between $\alpha$CDM and $w$CDM are included in the form $\bar{C}^{xx}_\ell=C^{xx}_{\ell\ \alpha{\rm CDM}}/C^{xx}_{\ell\ w{\rm CDM}}$, except $\bar{C}^{\rm TE}_\ell$ normalised with the temperature angular power spectrum.
• Figure 4: Upper panels: The matter power spectra $P(k)$ in $\Lambda$CDM and $b$CDM models are shown, separately for $\Omega_{\rm DR}=10^{-5}$ and $\Omega_{\rm DR}=10^{-6}$ and different values of the interaction parameter $b$. In the left (right) panel, dashed grey lines indicate the $P(k)$ corresponding to $\Omega_{\rm DR}=10^{-6}$ ($\Omega_{\rm DR}=10^{-5}$) for better illustration of the effects of the two parameters. We also show the ratio of the power spectra relative to $\Lambda$CDM, where we can see how there is the suppression controlled by $b$ below a scale determined by $\Omega_{\rm DR}$. Lower panels: The matter power spectrum $P(k)$ in $\alpha$CDM is displayed for different values of the interaction parameter $\alpha$. The case $\alpha=0$ corresponds to $w$CDM with $w=-0.98$. The $b$CDM models with $\Omega_{\rm DR}=10^{-5},10^{-6}$ and $b=-1$ are also included for comparison.
• Figure 5: Observational constraints on the $b$CDM model when using Planck2018 and BAO data (yellow), Planck2018, BAO and SnIa data (green), Planck2018, BAO and Planck SZ data (grey) and all the previous data sets (purple). We see how including the Planck SZ data is crucial to constrain the interaction parameter $b$. With the SZ data, the contours in the $\sigma_8$ - $\Omega_m$ plane is also shifted towards the region with smaller values of $\sigma_8$.