Luminous red galaxies (LRGs) are much rarer and more massive than L* galaxies. Coupled with their extreme colours, LRGs therefore provide a demanding testing ground for the physics of massive galaxy formation. We present the first self-consistent predictions for the abundance and properties of LRGs in hierarchical structure formation models. We test two published models which use quite different mechanisms to suppress the formation of massive galaxies: the Bower et al. (2006) model, which invokes ``AGN-feedback to prevent gas from cooling in massive haloes, and the Baugh et al. (2005) model which relies upon a ``superwind to eject gas before it is turned into stars. Without adjusting any parameters, the Bower et al. model gives an excellent match to the observed luminosity function of LRGs in the SDSS (with a median redshift of z=0.24) and to their clustering; the Baugh et al. model is less successful in these respects. Both models fail to match the observed abundance of LRGs at z=0.5 to better than a factor of ~2. In the models, LRGs are typically bulge dominated systems with M* of ~2x10^11 h^{-1} M_sun and velocity dispersions of ~250 km s^{-1}. Around half of the stellar mass in the model LRGs is already formed by z~2.2 and is assembled into one main progenitor by z~1.5; on average, only 25% of the mass of the main progenitor is added after z~1. LRGs are predicted to be found in a wide range of halo masses, a conclusion which relies on properly taking into account the scatter in the formation histories of haloes. Remarkably, we find that the correlation function of LRGs is predicted to be a power law down to small pair separations, in excellent agreement with observational estimates. Neither the Bower et al. nor the Baugh et al. model is able to reproduce the observed radii of LRGs.
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