Second-Order Gauge-Invariant Cosmological Perturbation Theory: Current Status
Figure 2
The second-kind gauge is a point-identification between the physical spacetime and the background spacetime on the extended manifold . Through (5), we implicitly assume the existence of a point-identification map between and . 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 and “” is same (). We may also choose the gauge so that and “” is same (). These are different gauge choices. The gauge transformation is given by the diffeomorphism .