Astronomy & Astrophysics

Table 1: Three tables listing the contributions of the different couplings in Sect. 3 to the interaction terms I⁰_i, I²_i, I³_ij and the mean interaction rate $\left\langle \Phi_i \right\rangle$ sorted by the coupling constants; they are required by Eqs. (36) to (40). A_i corresponds to a constant galaxy production/destruction, B_i^l couples galaxy field n_l to n_i (linear), C_i n_i to the dark matter field $\rho _{\rm m}$ (linear), D_i^lscouples n_l and n_s to n_i (quadratic), E_i couples $\rho _{\rm m}^2$ to n_i (quadratic), and F_i^l couples n_i to n_l and the dark matter field $\rho _{\rm m}$ (quadratic). The whole expression contributing is the product between the coupling constant, first column, and the expression in the second column or third column. Different contributions from different couplings are just added; we are using Einstein's summation convention for the variables l and s. Note that we have the special case $r_{ii}\equiv 1$ by definition of the correlation parameter. The bias parameters $\widehat{b_ir_i}$ and $\widehat{b_jb_jr_{ij}}$ , and $\left\langle \delta_{\rm m}^2 \right\rangle$ are explained in Sect. 3. They are only needed for modelling the mean galaxy density in the presence of quadratic couplings.