Abstract
The cosmological problem is studied here starting from a metric with a variable scale factor for time and two different ones for space, noted R for ordinary space and S for the extra dimensions. Once R has been obtained from physical principles, one is left for S with a differential equation which can be solved through Lie group analysis and dynamical systems theory, and a frequent use of computer algebra has been made in the ensuing calculations. This leads to a good agreement with the recent observational results relating to distant supernovae. However, the solution obtained for S is particularly simple if spacetime has a dimension at least equal to ten, a result to be compared with those given by superstring or M theories.
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