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Geodesically complete cyclic cosmologies and entropy
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We demonstrate that there exists a class of cyclic cosmological models, such that these models can in principle solve the problem of the entropy growth, and are at the same time geodesically complete. We thus show that some recently stated conclusions, according to which cyclic cosmologies solving the problem of entropy growth can not be geodesically complete due to the Borde-Guth-Vilenkin (BGV) theorem, are not justified. We also add a short conceptual discussion on entropy and cyclic cosmology, and present a detailed analysis of entropy density growth during periodic and non-periodic evolution for cyclic cosmologies.
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The BGV Theorem and the Null Convergence Condition
NCC plus ³R≤0 imply BGV for shear-free geodesic orthogonal foliations, but shear and non-geodesic threading make the BGV expansion directional and can evade that guarantee.
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