Clarifying the effects of interacting dark energy on linear and nonlinear structure formation processes

TL;DR

This study investigates direct interactions between Dark Energy and Cold Dark Matter by using modified N-body simulations to disentangle linear and nonlinear effects such as a fifth-force, time-varying CDM masses, and a velocity-dependent acceleration. By comparing two normalization schemes and selectively suppressing individual effects at different epochs, the authors show that the velocity-dependent acceleration is the leading nonlinear driver of reduced halo concentrations, while mass variation has a smaller but non-negligible impact and the fifth-force largely affects baryon bias rather than inner halo structure. The work resolves apparent discrepancies in prior studies by demonstrating that mixing linear and nonlinear influences (as occurs when suppressing effects from the start) can misattribute the dominant nonlinear mechanism. The results reinforce the Baldi et al. findings and emphasize the importance of late-time, nonlinear-focused comparisons for interpreting structure formation in coupled dark energy cosmologies.

Abstract

We present a detailed numerical study of the impact that cosmological models featuring a direct interaction between the Dark Energy component that drives the accelerated expansion of the Universe and Cold Dark Matter can have on the linear and nonlinear stages of structure formation. By means of a series of collisionless N-body simulations we study the influence that each of the different effects characterizing these cosmological models - which include among others a fifth force, a time variation of particle masses, and a velocity-dependent acceleration - separately have on the growth of density perturbations and on a series of observable quantities related to linear and nonlinear cosmic structures, as the matter power spectrum, the gravitational bias between baryons and Cold Dark Matter, the halo mass function and the halo density profiles. We perform our analysis applying and comparing different numerical approaches previously adopted in the literature, and we address the partial discrepancies recently claimed in a similar study by Li & Barrow (2010b) with respect to the first outcomes of Baldi et al. (2010), which are found to be related to the specific numerical approach adopted in the former work. Our results fully confirm the conclusions of Baldi et al. (2010) and show that when linear and nonlinear effects of the interaction between Dark Energy and Cold Dark Matter are properly disentangled, the velocity-dependent acceleration is the leading effect acting at nonlinear scales, and in particular is the most important mechanism in lowering the concentration of Cold Dark Matter halos.

Figures (6)

• Figure 1: (Color online) Left panel: The background evolution of a standard $\Lambda$CDM model and of an interacting DE model with $\beta = 0.24$. In this example we have not included the uncoupled fraction of baryonic matter to simplify the plot. The figure shows the evolution of the dimensionless density in radiation (green), matter (black) and dark energy (red) as a function of the e-folding time (defined as the logarithm of the scale factor $a$) for $\Lambda$CDM (solid) and interacting DE (dashed). The smaller plot shows the ratio of the same quantities to the $\Lambda$CDM case. Right panel: The ratio of the Hubble function of the same two models with respect to $\Lambda$CDM as a function of the e-folding time. A larger Hubble function with respect to $\Lambda$CDM is consistent with all previous studies on interacting DE and EDE, as explained in the text.
• Figure 2: (Color online) The evolution of CDM particle mass as a function of redshift in all the simulations of Table \ref{['tab:simulations']}. The curved line correponds to the evolution in the full interacting DE model. This evolution can be stopped at different times in the different simulations according to the different numerical methods discussed in the text.
• Figure 3: (Color online) The matter power spectrum of $\Lambda$CDM (black) and interacting DE (red) as a function of inverse scale $k$ at different redshifts. The upper panels show the test simulations run suppressing specific effects of the DE-CDM interaction right from the start of the simulations. Lower panels show the results of simulations with a suppression only during the latest stages of structure formation, i.e.$\,$ for $z\le z_{{\rm nl}}=2$. Clearly, the large scatter present in the upper panels witnesses the superposition of linear and nonlinear effects arising as a consequence of the procedure adopted in simulations S2-S6. The method used in simulations S7-S9 is clearly more suitable to compare the nonlinear effects of interacting DE models, and shows how the velocity-dependent acceleration (blue) is the most relevant mechanism in the suppression of small-scale power in these models.
• Figure 4: (Color online) The evolution of the gravitational bias $R(k,z)$ as a function of inverse scale $k$ for the $\Lambda$CDM model (black) and the interacting DE scenario (red). Upper plots show the results of the test simulations S2-S6 with high-redshift suppression of the individual effects, while lower panels show the results of simulations S7-S9 with suppression only for $z\le z_{{\rm nl}}=2$. The leading role of the fifth force (green) in determining a gravitational bias clearly appears in both sets of simulations.
• Figure 5: (Color online) The cumulative mass functions of CDM halos in $\Lambda$CDM (black) and interacting DE (red) models at $z=1$ and $z=0$. The large scatter of the different halo mass functions in the upper panels is due to the high-redshift suppression of the individual effects of the DE-CDM interaction in the simulations S2-S6. The same scatter does not appear if a low-redshift suppression is adopted.