Review Article

Second-Order Gauge-Invariant Cosmological Perturbation Theory: Current Status

Figure 2

The second-kind gauge is a point-identification between the physical spacetime 𝜆 and the background spacetime 0 on the extended manifold 𝒩 . Through (5), we implicitly assume the existence of a point-identification map between 𝜆 and 0 . However, this point-identification is not unique by virtue of the general covariance in the theory. We may chose the gauge of the second-kind so that 𝑝 0 and “ 𝑝 𝜆 is same ( 𝒳 𝜆 ). We may also choose the gauge so that 𝑞 0 and “ 𝑝 𝜆 is same ( 𝒴 𝜆 ). These are different gauge choices. The gauge transformation 𝒳 𝜆 𝒴 𝜆 is given by the diffeomorphism Φ = 𝒳 𝜆 1 𝒴 𝜆 .
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