Coupled Quintessence and the Halo Mass Function

TL;DR

The paper investigates how a light quintessence field coupled to cold dark matter modifies the halo mass function. It combines three quintessence potentials with semi-analytic mass functions (PS, ST, Jenkins) and two approaches to the collapse threshold δ⋆(z), then uses CosmoMC to fit model parameters to CMB+BAO+SN1a+H0 data. The results show that coupling direction and strength, together with the potential shape, can either suppress or enhance the abundance of massive halos, with some coupled models remaining compatible with data and potentially addressing tensions posed by massive high‑redshift clusters. The work emphasizes the sensitivity of high‑mass, high‑z clusters to dark‑energy–dark‑matter coupling and δ⋆(z) modelling, and highlights the need for cosmologically consistent parameter choices and accurate collapse modelling for robust predictions.

Abstract

A sufficiently light scalar field slowly evolving in a potential can account for the dark energy that presently dominates the universe. This quintessence field is expected to couple directly to matter components, unless some symmetry of a more fundamental theory protects or suppresses it. Such a coupling would leave distinctive signatures in the background expansion history of the universe and on cosmic structure formation, particularly at galaxy cluster scales. Using semi--analytic expressions for the CDM halo mass function, we make predictions for halo abundance in models where the quintessence scalar field is coupled to cold dark matter, for a variety of quintessence potentials. We evaluate the linearly extrapolated density contrast at the redshift of collapse using the spherical collapse model and we compare this result to the corresponding prediction obtained from the non--linear perturbation equations in the Newtonian limit. For all the models considered in this work, if there is a continuous flow of energy from the quintessence scalar field to the CDM component, then the predicted number of CDM haloes can only lie below that of $Λ$CDM, when each model shares the same cosmological parameters today. In the last stage of our analysis we perform a global MCMC fit to data to find the best fit values for the cosmological model parameters. We find that for some forms of the quintessence potential, coupled dark energy models can offer a viable alternative to $Λ$CDM in light of the recent detections of massive high--$z$ galaxy clusters, while other models of coupled quintessence predict a smaller number of massive clusters at high redshift compared to $Λ$CDM.

Figures (10)

• Figure 1: Left panel: The evolution of the quintessence field equation of state parameter $w_{\phi}=P_{\phi}/\rho_{\phi}$ for the three potentials for a variety of coupling strengths $\beta$. Right panel: The redshift evolution of the Hubble parameter $H(z)$ in the 2EXP and SUGRA models. In the lower panel we compare to the evolution of $H(z)$ in $\Lambda$CDM by plotting the ratio. For the AS model, $H(z)$ is identical to $\Lambda$CDM over the redshift range of interest, for all coupling strengths considered in this study.
• Figure 2: The cosmological evolution of the energy density parameters $\Omega_{i}$ in the 2EXP (left panel) and AS (right panel) models: $\Omega_{\gamma}(a)$ (solid), $\Omega_{\rm c}(a)$ (short--dashed), $\Omega_{\rm b}(a)$ (long--dashed) and $\Omega_{\phi}(a)$ (dot--dashed). The black (red) lines are for $\beta=0 (0.1)$. Note that $z_{\text{eq}}$ occurs earlier (later) in the coupled 2EXP(AS) cosmology as a result of its higher (lower) CDM density at early times.
• Figure 3: The cosmological evolution of the energy density parameters $\Omega_{i}$ for the SUGRA potential. Line types as in Fig. \ref{['fig:2EXPOmegas']}. Notice that $z_{{\rm eq}}$ occurs later in the coupled cosmology as a result of lower CDM density at early times.
• Figure 4: Evolution of the ratio of the CDM density contrast to $\Lambda$CDM, $\delta_{{\rm c}}/\delta_{{\rm c}\,\Lambda{{\rm CDM}}}$, for the coupled 2EXP (left panel) and SUGRA (right panel) models. These figures were obtained by numerically integrating Eqs. (\ref{['bgrowthrateCQ']}) and (\ref{['CDMgrowthrateCQ']}). Notice that the scales are different.
• Figure 5: The linear (total) matter power spectrum at $z=0$, $P_{0}(k)$, generated using the CAMB computer software for the models under consideration. We show various coupling strengths and compare to the linear power spectrum of $\Lambda$CDM in the lower panels. Left panel: 2EXP model. Middle panel: AS model. Right panel: SUGRA model. Note that all spectra have been normalised to CMB fluctuations, which are on larger scales than included in the figure.