Cosmic anisotropic hair of nonlocal RT gravity

Nonlocal RT gravity has proven effective in explaining the late-time cosmic acceleration while remaining consistent with local gravity tests. However, most previous cosmological studies of this theory have assumed an isotropic background, which may not fully capture the slight anisotropies suggested by current observations, such as those inferred from Type Ia supernovae data. In this paper, we investigate the dynamical evolution of an anisotropic Bianchi type I universe within the framework of nonlocal RT gravity. By introducing six dimensionless variables, we construct the corresponding dynamical system and perform a detailed phase-space analysis. An unexpected finding is that, contrary to many dark energy models and modified gravity theories in which anisotropies decay with time, nonlocal RT gravity predicts a growth of cosmic anisotropy. This behavior poses a challenge to the cosmic no-hair theorem within the nonlocal RT gravity scenario.