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David H. Lyth helped establish when large-scale cosmological curvature is conserved. With David Wands, Karim A. Malik and Andrew R. Liddle, he showed that negligible non-adiabatic pressure perturbations preserve the uniform-density curvature perturbation when spatial-gradient effects are negligible.^[ref]

The result specifies when primordial fluctuations can be carried forward without solving every intervening gravitational detail.

David Wands and collaborators gave a conservation-based account of long-wavelength fluctuations in linear cosmological perturbation theory. Their 2000 work treated slowly varying regions as locally homogeneous expanding universes and identified the conditions for conserved uniform-density curvature perturbations, without selecting particular gravitational field equations.^[ref]

The important qualifications are negligible spatial gradients and negligible non-adiabatic pressure perturbations; large wavelength alone is insufficient.

Karim A. Malik developed the treatment of gauge-invariant cosmological curvature with David Wands, David H. Lyth and Andrew R. Liddle. Their 2000 analysis derived large-scale evolution from stress-energy conservation, exposing how a non-adiabatic pressure perturbation can change the uniform-density curvature perturbation.^[ref]