$\chi \mathrm{S}\mathrm{B}$ of cascading gauge theory in de Sitter

$\mathcal{N}=1$ supersymmetric $SU(N)\times SU(N+M)$ cascading gauge theory of Klebanov et.al spontaneously breaks chiral symmetry in Minkowski space-time. We demonstrate that in de Sitter space-time the chiral symmetry breaking occurs for the values of the Hubble constant $H\lesssim 0.7\mathrm{\Lambda }$, as well as in a narrow window $0.92(1)\mathrm{\Lambda }\le H\le 0.92(5)\mathrm{\Lambda }$. We give a precise definition of the strong coupling scale $\mathrm{\Lambda }$ of cascading gauge theory, which is related to the glueball mass scale in the theory $m_{glueball}$ and the asymptotic string coupling $g_s$ as $\mathrm{\Lambda }\sim g_s^{1\mathrm{/}2}{m}_{glueball}$.