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Fig. 1

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Cluster temperature-distribution function in the local and distant universe. Triangles are our estimation of the temperature distribution function. The stars represent the estimated temperature distribution function at high redshift from the 400 deg2 sample restricted to the redshift range [0.4–0.6]. The continuous line corresponds to the predicted temperature distribution adjusted to fit CMB, SNIa, LSS, and the local temperature distribution function. The predictions for this model at redshift 0.5 (the lower continuous line) are far in excess of the abundances estimated from observations. For visual comparison, the dashed lines are the corresponding predictions with an evolving mass-temperature relation, Eq. (6), with α =  − 1 (not fitted).

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