Integrability of irrotational silent cosmological models

Abstract

We revisit the issue of integrability conditions for the irrotational silent cosmological models. We formulate the problem both in 1+3 covariant and 1+3 orthonormal frame notation, and show there exists a series of constraint equations that need to be satisfied. These conditions hold identically for FLRW--linearised silent models, but in the exact non--linear case they are very complex in form. We conjecture there are no spatially inhomogeneous solutions where the Weyl curvature tensor is of algebraic Petrov type I, and indicate further issues that await clarification.