Constraining interacting dark energy models with the halo concentration-mass relation

The interacting dark energy (IDE) model is a promising alternative cosmological model which has the potential to solve the fine-tuning and coincidence problems by considering the interaction between dark matter and dark energy. Previous studies have shown that the energy exchange between the dark sectors in this model can significantly affect the dark matter halo properties. In this study, utilising a large set of cosmological $N$-body simulations, we analyse the redshift evolution of the halo concentration-mass ($c$-$M$) relation in the IDE model, and show that the $c$-$M$ relation is a sensitive proxy of the interaction strength parameter $\xi_2$, especially at lower redshifts. Furthermore, we construct parametrized formulae to quantify the dependence of the $c$-$M$ relation on $\xi_2$ at redshifts ranging from $z=0$ to $0.6$. Our parametrized formulae provide a useful tool in constraining $\xi_2$ with the observational $c$-$M$ relation. As a first attempt, we use the data from X-ray, gravitational lensing, and galaxy rotational curve observations and obtain a tight constraint on $\xi_2$, i.e. $\xi_2 = 0.071 \pm 0.034$. Our work demonstrates that the halo $c$-$M$ relation, which reflects the halo assembly history, is a powerful probe to constrain the IDE model.