Disentangling interacting dark energy cosmologies with the three-point correlation function

We investigate the possibility of constraining coupled dark energy (cDE) cosmologies using the three-point correlation function (3PCF). Making use of the CoDECS N-body simulations, we study the statistical properties of cold dark matter (CDM) haloes for a variety of models, including a fiducial $\Lambda$CDM scenario and five models in which dark energy (DE) and CDM mutually interact. We measure both the halo 3PCF, $\zeta(\theta)$, and the reduced 3PCF, $Q(\theta)$, at different scales ($2<r\,[$Mpc\h$]<40$) and redshifts ($0\leq z\leq2$). In all cDE models considered in this work, $Q(\theta)$ appears flat at small scales (for all redshifts) and at low redshifts (for all scales), while it builds up the characteristic V-shape anisotropy at increasing redshifts and scales. With respect to the $\Lambda $CDM predictions, cDE models show lower (higher) values of the halo 3PCF for perpendicular (elongated) configurations. The effect is also scale-dependent, with differences between $\Lambda$CDM and cDE models that increase at large scales. We made use of these measurements to estimate the halo bias, that results in fair agreement with the one computed from the two-point correlation function (2PCF). The main advantage of using both the 2PCF and 3PCF is to break the bias$-\sigma_{8}$ degeneracy. Moreover, we find that our bias estimates are approximately independent of the assumed strength of DE coupling. This study demonstrates the power of a higher-order clustering analysis in discriminating between alternative cosmological scenarios, for both present and forthcoming galaxy surveys, such as e.g. BOSS and Euclid.