Probing the Type 3 interacting dark-energy model using matter pairwise velocity

Abstract

Dark sector interactions can be explored via the so-called Type 3 model where dark matter and dark energy exchange momentum only, so as to minimize deviations from the $Λ$CDM background expansion history. Using N-body simulations, we analyze the imprint of Type 3 model parameters, the momentum exchange coupling constant $β$ and the slope of scalar field potential $λ$, on large-scale structure observables, particularly the matter pairwise velocity statistics. We find that the effects of $β$ ($<0$) and $λ$ on the mean matter peculiar pairwise velocity and velocity dispersion are degenerate. Our results highlight the potential of velocity statistics as a probe of dark sector interactions and underscore the importance of disentangling $β$ and $λ$ in cosmological analyses.

Figures (7)

• Figure 1: 2D overdensity distributions of CDM at redshift $z = 0$. The left, center, and right columns correspond to parameter configurations A1 ($\beta=-1.4$, $\lambda=0.6$), A7 ($\beta=-0.5$, $\lambda=0.6$), and A9 ($\beta=-0.5$, $\lambda=1.4$), respectively. Each row provides a progressively enlarged view of the regions of interest (white squares in top two rows) with the spatial scale and slice thickness indicated below the figures. The bottom row highlights a host halo enclosed by a white circle corresponding to its virial radius ($R_{\text{vir}}$). The corresponding virial mass ($M_{\text{vir}}$) and $R_{\text{vir}}$ values are annotated in the upper-left corners. The density scale is indicated by the color bars.
• Figure 2: Mean particle-particle peculiar pairwise velocity $v_{\mathrm{pp}}$ (top panel) and velocity dispersion $\sigma_{\mathrm{pp}}$ (bottom panel). The left and right columns show the pairwise velocity statistics for varying $\beta$ (with $\lambda=0.6$) and $\lambda$ (with $\beta=-0.5$), respectively, compared to the uncoupled case A0 with $\beta = 0, \, \lambda = 0.6$ (purple lines). Subpanels display percentage deviations from the fiducial configuration's (A0), $\frac{\Delta [v/\sigma]_{\mathrm{pp}}}{[v/\sigma]_{\mathrm{pp,0}}}= \frac{[v/\sigma]_{\mathrm{pp}} (\text{other cases}) - [v/\sigma]_{\mathrm{pp}} (\mathrm{A0})}{[v/\sigma]_{\mathrm{pp}} (\mathrm{A0})}$. The dashed line in the top left panel represents the linear approximation, and the star in the bottom panel denotes the CEE approximation, both for A0.
• Figure 3: $\Delta R^{v}_{\text{p1}}$ (upper left), $\Delta R^{\sigma}_{\text{p2}}$(upper right), $\Delta R^{v}_{\text{h2}}$ for light halos (lower left), and $\Delta R^{\sigma}_{\text{h2}}$ for heavy halos (lower right), respectively. Displayed as a function of $\lambda$, the data obtained from the simulations, along with their error bars, are fitted to a three-variable linear regression (dashed lines), with different colors corresponding to different $\beta$.
• Figure 4: Mean halo-halo peculiar pairwise velocity $v_{\mathrm{hh}}$ (top panels) and velocity dispersion $\sigma_{\mathrm{hh}}$ (bottom panels), for light (dashed lines) and heavy (solid lines) halos. The left and right columns show the pairwise velocity statistics for varying $\beta$ (with $\lambda=0.6$) and $\lambda$ (with $\beta=-0.5$), respectively, compared to the uncoupled case A0 with $\beta = 0$, $\lambda = 0.6$ (purple lines). Subpanels display percentage deviations from the fiducial's, with $\frac{\Delta [v/\sigma]_{\mathrm{hh}}}{[v/\sigma]_{\mathrm{hh,0}}}= \frac{[v/\sigma]_{\mathrm{hh}} (\text{other cases}) - [v/\sigma]_{\mathrm{hh}} (\mathrm{A0})}{[v/\sigma]_{\mathrm{hh}} (\mathrm{A0})}$.
• Figure 5: Mean particle-particle peculiar pairwise velocity $v_{\mathrm{pp}}$ (upper panel) and mean peculiar particle-particle pairwise velocity dispersion $\sigma_{\mathrm{pp}}$ (lower panel). The colors in the plots correspond to measurements using different fractions of randomly selected CDM particles from the simulations. The subpanels below the mean peculiar pairwise velocity and velocity dispersion plots show their fractional deviations relative to measurements in which $10\%$ of CDM particles have been selected.