can the sort of perturbation theory used in cosmology be used to describe the surface of the earth?
Mark,
Could you clarify exactly what you are referring to?
The surface of the Earth is well described by a number of methods (spherical Bessel functions, fractals, point meshes, etc.)
Yes, it can, but probably this will be less useful as the standard methods
used in practice.
The question sounds rather vague. Nevertheless, I'll try to present some thoughts.
1) In cosmology we use general relativity (GR). GR deals with internal geometry of space-time. Internal geometry is 4-dimensional geometry itself. It is not geometry of some surface in space of higher dimension.
2) The earth surface geometry is external geometry. It is geometry of 2-dimensional surface in 3-dimensional space. E.g. external geometry is able to distinguish a mountain and a ravine. From the point of view of internal geometry a mountain and a ravine are just the same.
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