Non-maximal Anosov representations from surface groups to ${\mathrm{S}\mathrm{O}}_0(2,3)$

We prove the representation given by a stable ${\alpha }_1$-cyclic parabolic ${\mathrm{S}\mathrm{O}}_0(2,3)$-Higgs bundle through the non-Abelian Hodge correspondence is $\{{\alpha }_2\}$-almost dominated. This is a generalization of Filip’s result on weight $3$ variation of Hodge structures and answers a question asked by Collier, Tholozan and Toulisse.