Abstract
We investigate the scale factor duality of the scalar–tensor theory in four and ten dimensions with matter. It is shown that when the pressure of the matter vanishes (γ = 0 for the equation of state p = γρ), the action is invariant under the duality. In addition, the action is invariant again under the change of the sign of the pressure (p→-p or γ→-γ). In higher dimensions, we distinguish the matter, e.g., in four dimensions px = γxρ and for extra six dimensions py = γy ρ. The scale factor duality in this case is that when γx = 0 the duality transformation acts on the four-dimensional scale factor and the dilaton with the extra dimensions intact while when γy = 0 it acts on the extra six dimensions and the dilaton with four dimensions intact.
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