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If the present acceleration of the universe is due to a cosmologicalconstant, \lambda, then the entropy of the microwave background is bounded. Itcannot exceed \lambda^{-3/4} \sim 10^{91}, which is much less than the entropyof empty de Sitter space \lambda^{-1} \sim 10^{122}. This is due to the limitedefficiency of storing entropy by local field theoretical degrees of freedom.The observed entropy of the microwave background is of O(10^{85}).Comment: 12 pages, 1 eps figure, Latex, references adde

The entropy of the microwave background and the acceleration of the universe