We obtain the analytic solution of the Friedmann equation for fully realistic
    cosmologies including radiation, non-relativistic matter, a cosmological
    constant $\lambda$ and arbitrary spatial curvature $\kappa$. The general
    solution for the scale factor $a(\tau)$, with $\tau$ the conformal time, is an
    elliptic function, meromorphic and doubly periodic in the complex $\tau$-plane,
    with one period along the real $\tau$-axis, and the other along the imaginary
    $\tau$-axis. The periodicity in imaginary time allows us to compute the
    thermodynamic temperature and entropy of such spacetimes, just as Gibbons and
    Hawking did for black holes and the de Sitter universe. The gravitational
    entropy favors universes like our own which are spatially flat, homogeneous,
    and isotropic, with a small positive cosmological constant.



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