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LCDM: Triumphs, Puzzles and Remedies

The consistency level of LCDM with geometrical data probes has been increasing with time during the last decade. Despite of these successes, there are some puzzling conflicts between LCDM predictions and dynamical data probes (bulk flows, alignment and magnitude of low CMB multipoles, alignment of quasar optical polarization vectors, cluster halo profiles). Most of these puzzles are related to the existence of preferred anisotropy axes which appear to be unlikely close to each other. A few models that predict the existence of preferred cosmological axes are briefly discussed.