Non-linear structure formation with elastic interactions in the dark sector

TL;DR

The paper investigates non-linear structure formation in a dark-sector model where dark matter and dark energy exchange momentum but not energy, implemented via a covariantised elastic interaction $Q^ u=ar{\alpha}(u^ u_{ m de}-u^ u_{ m dm})$ with a single coupling parameter $\a$. By embedding this into RAMSES and simulating two-component matter (dark matter and baryons) in a $w$CDM background, the study finds that linear theory shows a suppression of growth, while non-linear scales exhibit enhanced dark-matter clustering, yielding more compact halos and a non-constant DM–baryon density ratio; very massive halos are suppressed while smaller halos remain largely unaffected. The results reveal that, although baryons remain good tracers of the dark matter velocity field and continue to reside in DM potential wells, the internal halo structure and abundance of the most massive objects are altered, offering distinctive observational signatures. Overall, the work demonstrates that elastic momentum-transfer models imprint measurable non-linear effects on the power spectrum and halo properties, providing a concrete framework and tool for confronting such scenarios with current and future large-scale structure data.

Abstract

Cosmological models where dark matter interacts with dark energy via a pure momentum transfer and with no energy exchange (i.e. elastic) provide compelling scenarios for addressing the apparent lack of structures at low redshift. In particular, it has been shown that measurements of $S_8$ may show a statistically significant preference for the presence of elastic interactions. In this work we implement a specific realisation of these scenarios into an $N$-body code to explore the non-linear regime. We include two populations of particles to describe the interacting dark matter and the non-interacting baryons respectively. On linear scales we recover the suppression of structures obtained from Boltzmann codes, while non-linear scales exhibit an enhancement of the matter power. We find that fewer massive halos are formed at low redshift as a consequence of the elastic interaction and that dark matter halos are more compact than in the standard model. Furthermore, the ratio of dark matter and baryons density profiles is not constant. Finally, we corroborate that baryons efficiently cluster around dark matter halos so they provide good tracers of the dark matter velocity field despite the presence of the interaction. This shows that the interaction is not sufficiently strong as to disrupt virialised structures.

Figures (8)

• Figure 1: Velocity divergence $\theta$ today of dark energy (blue), dark matter (red) and the non-interacting baryons (black) for different values of the coupling parameter $\alpha$. For the case analysed here with coupling parameter $\alpha=1$, we can corroborate that the velocity of dark energy is much smaller than those of baryons and dark matter, thus justifying approximation done, $v_{\rm dm}\gg v_{\rm de}$ and $v_{\rm b}\gg v_{\rm de}$, of neglecting dark energy velocities for the scales relevant for our simulations.
• Figure 2: The matter power spectrum for different redshifts computed from the modified version of CLASS with HALOFIT and from RAMSES (upper panels) and the ratio $P(k)^\texttt{HALOFIT}/P(k)^\texttt{RAMSES}-1$ in order to show to which precision HALOFIT can predict the non-linear scales (lower panels).
• Figure 3: Relative difference for the matter power spectra between the covariantised dark Thomson-like interacting model and the $\Lambda$CDM model at different redshifts computed from the simulation output using all the particles (solid lines) and using the linear solver CLASS (dash-dotted lines).
• Figure 4: The matter power spectrum for $\Lambda$CDM model (left) and for the covariantised dark Thomson-like interacting model at $z=0.05$ computed from the simulation output using all the particles (dot-points), only dark matter particles (blue line) and only baryons particles (red line).
• Figure 5: Spatial distribution of the halos found by MatchMaker in the simulation box. Each dot is a halo whose colour and dot-size are proportional to the halo mass.