# Weyl-curvature in cosmology

10 Mar 2021Is the Weyl-tensor zero for FLRW-cosmologies? If yes, whatâ€™s the physical reason?

FLRW-cosmologies are maximally symmetric spacetimes, where the Riemann-curvature can be expressed solely in terms of the Ricci-curvature: \(R_{\alpha\beta\mu\nu} = \frac{R}{12}\left(g_{\alpha\mu}g_{\beta\nu} - g_{\alpha\nu}g_{\beta\mu}\right),\) i.e. the Weyl-part of the curvature is zero, \(C_{\alpha\beta\mu\nu} = 0\). This is a consequence of the cosmological principle which says that the spacetime is homogeneous and isotropic.