In general relativity, the Newtonian gauge is a perturbed form of the Friedmann–Lemaître–Robertson–Walker line element.
The gauge freedom of general relativity is used to eliminate two scalar degrees of freedom of the metric, so that it can be written as: where the Latin indices a and b are summed over the spatial directions and
for non-relativistic matter and on scales where the expansion of the universe may be neglected.
The vector perturbations vanish in cosmic inflation and the tensor perturbations are gravitational waves, which have a negligible effect on physics except for the so-called B-modes of the cosmic microwave background polarization.
In a universe without anisotropic stress (that is, where the stress–energy tensor is invariant under spatial rotations, or the three principal pressures are identical) the Einstein equations sets
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