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We present cosmological solutions for (1+3+n)-dimensional steady stateuniverse in dilaton gravity with an arbitrary dilaton coupling constant w andexponential dilaton self-interaction potentials in the string frame. We focusparticularly on the class in which the 3-space expands with a time varyingdeceleration parameter. We discuss the number of the internal dimensions andthe value of the dilaton coupling constant to determine the cases that areconsistent with the observed universe and the primordial nucleosynthesis. The3-space starts with a decelerated expansion rate and evolves into acceleratedexpansion phase subject to the values of w and n, but ends with a Big Rip inall cases. We discuss the cosmological evolution in further detail for thecases w=1 and w=1/2 that permit exact solutions. We also comment on how theuniverse would be conceived by an observer in four dimensions who is unaware ofthe internal dimensions and thinks that the conventional general relativity isvalid at cosmological scales.

Late Time Acceleration of the 3-Space in a Higher Dimensional Steady State Universe in Dilaton Gravity