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出典:『Wikipedia』 (2011/04/07 10:32 UTC 版)

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In cosmological perturbation theory, the scalar-vector-tensor decomposition is a decomposition of the most general linearized perturbations of the Friedmann-Lemaitre-Robertson-Walker metric into components according to their transformations under spatial rotations. It was first discovered by E. M. Lifshitz in 1946. The general metric perturbation has ten degrees of freedom. The decomposition states that the evolution equations for the most general linearized perturbations of the Friedmann-Lemaitre-Robertson-Walker metric can be decomposed into four scalars, two divergence-free spatial vector fields (that is, with a spatial index running from 1 to 3), and a traceless, symmetric spatial tensor field with vanishing doubly and singly longitudinal components. The vector and tensor fields each have two independent components, so this decomposition encodes all ten degrees of freedom in the general metric perturbation. Using gauge invariance four of these components (two scalars and a vector field) may be set to zero.