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We present a method for constructing gauge-invariant cosmological perturbations which are gauge-invariant up to second order. As an example, we give the gauge-invariant definition of the second-order curvature perturbation on uniform density hypersurfaces. Using only the energy conservation equation, we show that this curvature perturbation is conserved at second order on large scales for adiabatic perturbations.
Malik et al. (Sat,) studied this question.
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