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We present a method to define second-order gauge-invariant curvature perturbations, indicating conservation on large scales.
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.
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Malik et al. (2004) studied this question.
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