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Daniel Mahler
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![Geometric meaning of $\nabla_{[i}(x^i \nabla_{j]}x^j)$ and $(\nabla_{[i}x^i )\nabla_{j]}x^j$](http://lh3.googleusercontent.com/proxy/FJ3sHyGZ6RkHBm3BF9phIn2vv2iaX3YNmhByd9aK7voPrUeP82txnhAz1-tet7ncc9NbPox2F1YeGTNuJfMgtFR1qMFQZtqkEOH5tJuvPchbBqd0OQ=s110-p)
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Eggs, brains & entropy
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Why does dark energy produce positive space-time curvature?
My understanding is that dark energy, or equivalently a positive cosmological constant, is accelerating the expansion of the universe and I have read that this gives empty space-time positive curvature, ie de Sitter geometry. I also understand that parallel geodesics converge when curvature is positive and diverge when it is negative. I would expect accelerating expansion of space to make parallel space-time geodesics diverge and thus make curvature negative. Is there a nice visual explanation why dark energy actually produces positive curvature?
My understanding is that dark energy, or equivalently a positive cosmological constant, is accelerating the expansion of the universe and I have read that this gives empty space-time positive curvature, ie de Sitter geometry. I also understand that parallel geodesics converge when curvature is positive and diverge when it is negative. I would expect accelerating expansion of space to make parallel space-time geodesics diverge and thus make curvature negative. Is there a nice visual explanation why dark energy actually produces positive curvature?
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