# The true time scale of the universe

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:
2. H.~Stephani et al, {\it Exact Solutions of Einstein’s Field Equations }, Cambridge University Press, 2003
3. S.~Weinberg, {\it Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity }, John Wiley \& Sons, New York (1972)
4. Robert~V.~Penney, Conformally flat zero-mass meson solutions of Einstein equations, Phys. Rev. D {\bf14}, 910 (1976)
5. Steven Weinberg, {\it The cosmological constant problem}, Rev. Mod. Phys. {\bf 61}, 1 (1989)
6. P. J. E. Peebles and Bharat Ratra, {\it The cosmological constant and dark energy},
Rev. Mod. Phys. {\bf 75}, 559 (2003)
7. N.~Aghanim, C.~Armitage-Caplan, M.~Arnaud, et al., {\it Planck 2015 results. XIII. Cosmological parameters.}, arXiv:1502.01589 [astro-ph.CO] (2015)