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Cosmological Perturbation Theory: How do perturbations transform?  

2011-10-08 13:51:30|  分类: cosmology |  标签: |举报 |字号 订阅

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Cosmological models are constructed in the frame of General Relativity, so the mathematical language we are using is tensor analysis.

In GR, we have metric tensor, 4-velocity, energy-momentum tensor ,etc. General relativity tells us how these quantities transform under a general coordinate transformation.  The equations which are expressed in tensors will maintain their forms in an arbitrary coordinate system, which corresponds to the general covariance of physical laws.

Because the tensors are local quantities, and we require that the transformation laws will be the same when perturbations are present, this is our starting point.

We first write down the full form of the relevant tensor transformation, then we expand all the quantities to first order(anyway, to which order is your interest), subtract the unperturbed parts from the full form and omit the higher order small quantities, and finally we get what we want!

This is quite easy, isn't it?


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