Review Article

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

Figure 1

(a) The second term 𝜆 𝜉 1 ( 𝑝 ) in (4) is the vector which points from the point 𝑥 𝜇 ( 𝑝 ) to the point 𝑥 𝜇 ( 𝑞 ) in the sense of the first-order correction. (b) If we look at the neighborhood of the point 𝑥 𝜇 ( 𝑞 ) in detail, the vector 𝜆 𝜉 1 ( 𝑝 ) may fail to point to 𝑥 𝜇 ( 𝑞 ) in the sense of the second order. Therefore, it is necessary to add the second-order correction ( 1 / 2 ) 𝜆 2 ( 𝜉 𝜇 2 + 𝜉 𝜈 1 ( 𝑝 ) 𝜕 𝜈 𝜉 𝜇 1 ( 𝑝 ) ) .
576273.fig.001a
(a)
576273.fig.001b
(b)