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In this paper, the effect of the space-time dimension on effectivethermodynamic quantities in (n+2)-dimensional Reissoner-Nordstrom-de Sitterspace has been stud ied. Based on derived effective thermodynamic quantities,conditions for the phase transition are obtained. The result shows that theaccelerating cosmic expansion can be attained by the entropy force arisen fromthe interaction between horizons of black holes and our universe, whichprovides a possible way to explain the physical mechanism for the acceleratingcosmic expansion.

Phase transition and entropy force between two horizons in (n+2)-dimensional de Sitter space