String cosmology coupled to Weyl-integrable geometry

The requirement that the laws of physics must be invariant under point-dependent transformations of the units of length, time, and mass is used as a selection principle while studying different generic effective theories of gravity. Thereof theories with non-minimal coupling of the dilaton both to the curvature and to the Lagrangian of the matter fields seem to represent the most viable low-energy [and low-curvature] description of gravity. Consequently, the cosmological singularity problem is treated within the context of string cosmology with non-minimal coupling of the dilaton to a barotropic gas of solitonic p-brane. The results obtained are to be interpreted on the grounds of Weyl-integrable geometry. The implications of these results for the Mach's principle are briefly discussed.