The CoDECS project: a publicly available suite of cosmological N-body simulations for interacting dark energy models

TL;DR

CoDECS investigates how a direct coupling between Dark Energy and Cold Dark Matter affects nonlinear structure formation. It deploys two public simulation suites, L-CoDECS and H-CoDECS, for five cDE models including constant, growing and bouncing couplings, with growth histories tied to CMB constraints. The study finds model dependent deviations in the nonlinear matter power spectrum, a scale dependent gravitational bias between baryons and CDM, and enhanced massive halo counts at high redshift for most models, while the bouncing SUGRA003 shows unique late time behavior. The public data release provides valuable resources for testing cDE predictions against current and future observations and enables community driven exploration of interacting dark energy scenarios.

Abstract

We present the largest set of N-body and hydrodynamical simulations to date for cosmological models featuring a direct interaction between the Dark Energy (DE) scalar field, responsible of the observed cosmic acceleration, and the Cold Dark Matter (CDM) fluid. With respect to previous works, our simulations considerably extend the statistical significance of the simulated volume and cover a wider range of different realizations of the interacting DE scenario, including the recently proposed bouncing coupled DE model. Furthermore, all the simulations are normalized in order to be consistent with the present bounds on the amplitude of density perturbations at last scattering, thereby providing the first realistic determination of the effects of a DE coupling for cosmological growth histories fully compatible with the latest Cosmic Microwave Background data. As a first basic analysis, we have studied the impact of the coupling on the nonlinear matter power spectrum and on the bias between the CDM and baryon distributions, as a function of redshift and scale. For the former, we have addressed the issue of the degeneracy between the effects of the coupling and other standard cosmological parameters, as e.g sigma_8, showing how the redshift evolution of the linear amplitude or the scale dependence of the nonlinear power spectrum might provide a way to break the degeneracy. For the latter, instead, we have computed the redshift and scale dependence of the bias in all our different models showing how a growing coupling or a bouncing coupled DE scenario provide much stronger effects with respect to constant coupling models. We refer to this vast numerical initiative as the COupled Dark Energy Cosmological Simulations project, or CoDECS, and we hereby release all the CoDECS outputs for public use through a dedicated web database, providing information on how to access and interpret the data.

Figures (8)

• Figure 1: Panel A: The equation of state parameter of DE $w_{\phi }$ as a function of redshift for all the models of the CoDECS project. The SUGRA003 model shows a "bounce" of the equation of state on the cosmological constant barrier $w_{\phi } = -1$ at $z_{\rm inv} \sim 6.8$ while all the other models asymptotically tend to $w_{\phi } = -1$ at $z\rightarrow 0$. Panel B: The upper plot shows the Hubble function in km/s/Mpc for all the models under investigation, while the lower plot shows the ratio of the Hubble function to the standard $\Lambda$CDM case. The maximum deviation is of about $6\%$ at $z\sim 5$ for the bouncing cDE model SUGRA003. Panel C: The CDM particle mass evolution as a function of redshift. All the models feature a monotonically decreasing mass, except the bouncing cDE model SUGRA003 that shows an inversion of the mass evolution in correspondence to the DE bounce. Panel D: The redshift evolution of the DE density parameter $\Omega _{\phi }$. The constant coupling models show a constant plateau at high z (the so called $\phi$-MDE regime), while the growing coupling model EXP008e3 shows a slowly evolving DE fraction Baldi_2011a. The bouncing cDE model SUGRA003 behaves like a standard constant coupling model in the early universe, but deviates from all the other models at recent epochs due to the DE bounce.
• Figure 2: Left: The growth factor $D_{+}(z)$ divided by the scale factor $a$ for all the models included in the CoDECS project, normalized at the redshift of the last scattering surface, $z_{\rm CMB}\approx 1100$. Right: The ratio of the growth factor of each cDE model to the standard $\Lambda$CDM case. All models start with the same amplitude as $\Lambda$CDM at $z_{\rm CMB}$ but significantly deviate from the standard evolution at later times. All the models show a monotonic increase of the deviation from $\Lambda$CDM, with the exception of the bouncing cDE model SUGRA003 that after an extended period of strongly enhanced growth inverts the trend in correspondence to the DE bounce, and recovers the $\Lambda$CDM amplitude at $z=0$Baldi_2011a.
• Figure 3: The CDM density distribution in a slice with size $1000\times 250$ Mpc$/h$ and thickness $30$ Mpc$/h$ as extracted from the L-CoDECS simulations of a few selected models. The middle slice shows the case of the standard $\Lambda$CDM cosmology, while the top slice is taken from the EXP003 simulation and the bottom slice from the bouncing cDE model SUGRA003. While the latter model shows basically no difference with respect to $\Lambda$CDM at $z=0$, due to the very similar value of $\sigma _{8}$ for the two models, clear differences in the overall density contrast and in the distribution of individual halos can be identified by eye for the EXP003 cosmology. (A higher resolution version of this figure is available online through the CoDECS website, see the Appendix)
• Figure 4: The gas density distribution during the formation process of a massive galaxy cluster as extracted from the H-CoDECS runs for the same three models shown in Fig. \ref{['fig:slice']}. Also in this case, differences in the overall density contrast and in the distribution of individual lumps are visible by eye when comparing the standard $\Lambda$CDM cosmology and the EXP003 cDE model at $z=0$. However, in this case the redshift evolution shown in the figure allows to identify differences also between $\Lambda$CDM and the bouncing cDE model SUGRA003 at higher redshifts, where the latter model appears more evolved and shows a more pronounced density contrast as compared to the standard cosmology. (A higher resolution version of this figure is available online through the CoDECS website, see the Appendix)
• Figure 5: The ratio of the nonlinear matter power spectrum to the standard $\Lambda$CDM cosmology for all the cDE models under discussion, as extracted from the L-CoDECS runs (solid), and the ratio of the nonlinear matter power spectrum for a $\Lambda$CDM model with the same $\sigma _{8}$ as the respective cDE model and the fiducial $\Lambda$CDM cosmology with $\sigma _{8}=0.809$, as computed by means of the HALOFIT routine of the public code CAMB (dotted). Although at linear scales the two quantities are completely degenerate at $z=0$, the different redshift evolution of the linear power spectrum amplitude allows to break the degeneracy. Furthermore, even at $z=0$, the nonlinear regime shows a clear difference between the effects of cDE and of a high value of $\sigma _{8}$ due to the distortion determined by the DE coupling on the matter power spectrum, be it either a suppression (as for constant and variable coupling models) or an enhancement (as for bouncing cDE).