  We investigate the effect of dark energy on the limits on the shear
anisotropy in spatially homogeneous Bianchi cosmological models obtained from
measurements of the temperature anisotropies in the cosmic microwave
background. We shall primarily assume that the dark energy is modelled by a
cosmological constant. In general, we find that there are tighter bounds on the
shear than in models with no cosmological constant, although the limits are
(Bianchi) model dependent. In addition, there are special spatially homogeneous
cosmological models whose rate of expansion is highly anisotropic, but whose
cosmic microwave background temperature is measured to be exactly isotropic at
one instant of time.
