A probability estimate for scalar-field homogeneity at the onset of inflation and slow contraction concludes that, after optimizing over initial spectra, inflation is vastly more likely than ekpyrosis to have the required smooth initial patch.
Asymptotic Behavior of Cosmologies with $\Lambda >0$ in 2+1 Dimensions
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We study, using Mean Curvature Flow methods, 2+1 dimensional cosmologies with a positive cosmological constant and matter satisfying the dominant and the strong energy conditions. If the spatial slices are compact with non-positive Euler characteristic and are initially expanding everywhere, then we prove that the spatial slices reach infinite volume, asymptotically converge on average to de Sitter and they become, almost everywhere, physically indistinguishable from de Sitter. This holds true notwithstanding the presence of initial arbitrarily-large density fluctuations and the formation of black holes.
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Probability of the Initial Conditions for Inflation and Slow Contraction
A probability estimate for scalar-field homogeneity at the onset of inflation and slow contraction concludes that, after optimizing over initial spectra, inflation is vastly more likely than ekpyrosis to have the required smooth initial patch.