The true time scale of the universe

author: Daniel L. Miller

1. Cosmological models are typically written for synchronous coordinates $g_{00}=1$, $g_{0 \alpha}=g_{\alpha 0}=0$. The conformally flat metric $t^{-2}\text{diag}(1,-1,-1,-1)$ solves the Einstein equation for empty space and non-zero cosmological constant. This is the collapsing cosmological model (it has negative Hubble constant). The Landau II volume gives the most comprehensive review of cosmological models. Bunch of other conformally flat solutions are in Stephani bible:
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