Abstract
We suggest a new explanation for the observed large scale flatness, homogeneity and isotropy of the universe. The basic ingredients are Einstein's theory of gravity and Hawking's method of computing the gravitational entropy. The new twist is provided by the boundary conditions we recently proposed for “big bang” type singularities dominated by conformal matter, enforcing CPT symmetry and analyticity. Besides allowing us to describe the big bang, these boundary conditions allow new gravitational instantons from which we calculate the total gravitational entropy Sg of cosmologies including radiation, dark energy and space curvature of either sign. We find Sg∼SΛ1/4Sr, where SΛ is the de Sitter entropy and Sr is the total entropy in radiation, which is extensive in the comoving spatial volume. Thus, Sg can be larger than SΛ and we show it is largest for universes which are spatially flat. Extending our analysis to include linearized perturbations, we show that, for a given set of globally conserved quantities, Sg is greatest for universes that are also homogeneous and isotropic on large scales.
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