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Cosmological perturbation theory studies departures of the metric tensor and matter fields from a homogeneous and isotropic FRW metric, order by order. Linear cosmological perturbation theory keeps only first-order terms. Higher orders describe nonlinear coupling between perturbations. Nonlinear cosmological perturbation theory also uses expansions that allow finite amplitudes, such as the long-wavelength approximation in cosmology.

This is the first-order sector of cosmological perturbation theory.

Linear cosmological perturbation theory expands the metric and matter fields to first order about a homogeneous and isotropic Friedmann-Lemaître-Robertson-Walker metric.