A de Sitter no-hair theorem for 3+1d cosmologies with isometry group forming 2-dimensional orbits

Paolo Creminelli; Or Hershkovits; Leonardo Senatore; András Vasy

doi:10.1016/j.aim.2023.109296

A de Sitter no-hair theorem for 3+1d cosmologies with isometry group forming 2-dimensional orbits

Paolo Creminelli, Or Hershkovits^*, Leonardo Senatore, András Vasy

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

We study, using Mean Curvature Flow methods, 3+1 dimensional cosmologies with a positive cosmological constant, matter satisfying the dominant and the strong energy conditions, and with spatial slices that can be foliated by 2-dimensional surfaces that are the closed orbits of a symmetry group. If these surfaces have non-positive Euler characteristic (or in the case of 2-spheres, if the initial 2-spheres are large enough) and also if the initial spatial slice is expanding everywhere, then we prove that asymptotically the spacetime becomes physically indistinguishable from de Sitter space on arbitrarily large regions of spacetime. This holds true notwithstanding the presence of initial arbitrarily-large density fluctuations.

Original language	American English
Article number	109296
Journal	Advances in Mathematics
Volume	434
DOIs	https://doi.org/10.1016/j.aim.2023.109296
State	Published - 1 Dec 2023

Bibliographical note

Funding Information:
We thank the anonymous referees whose invaluable comments had contributed tremendously to this paper. We thank Matt Kleban, Shamit Kachru, Brett Kotschwar, Jonathan Luk, Richard Schoen for discussions. OH has been partially supported by a Koret Foundation early career scholar award. LS is partially supported by Simons Foundation Origins of the Universe program (Modern Inflationary Cosmology collaboration) and LS by NSF award 1720397 . AV is partially supported by NSF awards DMS-1664683 and DMS-1953987 . PC would like to thank the Stanford Institute for Theoretical Physics for hospitality and support during part of this work. LS and AV would like to thank the International Center for Theoretical Physics for hospitality and support during part of this work.

Publisher Copyright:
© 2023 Elsevier Inc.

Keywords

Mean curvature flow
No hair

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10.1016/j.aim.2023.109296

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abstract = "We study, using Mean Curvature Flow methods, 3+1 dimensional cosmologies with a positive cosmological constant, matter satisfying the dominant and the strong energy conditions, and with spatial slices that can be foliated by 2-dimensional surfaces that are the closed orbits of a symmetry group. If these surfaces have non-positive Euler characteristic (or in the case of 2-spheres, if the initial 2-spheres are large enough) and also if the initial spatial slice is expanding everywhere, then we prove that asymptotically the spacetime becomes physically indistinguishable from de Sitter space on arbitrarily large regions of spacetime. This holds true notwithstanding the presence of initial arbitrarily-large density fluctuations.",

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AU - Vasy, András

N1 - Funding Information: We thank the anonymous referees whose invaluable comments had contributed tremendously to this paper. We thank Matt Kleban, Shamit Kachru, Brett Kotschwar, Jonathan Luk, Richard Schoen for discussions. OH has been partially supported by a Koret Foundation early career scholar award. LS is partially supported by Simons Foundation Origins of the Universe program (Modern Inflationary Cosmology collaboration) and LS by NSF award 1720397 . AV is partially supported by NSF awards DMS-1664683 and DMS-1953987 . PC would like to thank the Stanford Institute for Theoretical Physics for hospitality and support during part of this work. LS and AV would like to thank the International Center for Theoretical Physics for hospitality and support during part of this work. Publisher Copyright: © 2023 Elsevier Inc.

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N2 - We study, using Mean Curvature Flow methods, 3+1 dimensional cosmologies with a positive cosmological constant, matter satisfying the dominant and the strong energy conditions, and with spatial slices that can be foliated by 2-dimensional surfaces that are the closed orbits of a symmetry group. If these surfaces have non-positive Euler characteristic (or in the case of 2-spheres, if the initial 2-spheres are large enough) and also if the initial spatial slice is expanding everywhere, then we prove that asymptotically the spacetime becomes physically indistinguishable from de Sitter space on arbitrarily large regions of spacetime. This holds true notwithstanding the presence of initial arbitrarily-large density fluctuations.

AB - We study, using Mean Curvature Flow methods, 3+1 dimensional cosmologies with a positive cosmological constant, matter satisfying the dominant and the strong energy conditions, and with spatial slices that can be foliated by 2-dimensional surfaces that are the closed orbits of a symmetry group. If these surfaces have non-positive Euler characteristic (or in the case of 2-spheres, if the initial 2-spheres are large enough) and also if the initial spatial slice is expanding everywhere, then we prove that asymptotically the spacetime becomes physically indistinguishable from de Sitter space on arbitrarily large regions of spacetime. This holds true notwithstanding the presence of initial arbitrarily-large density fluctuations.

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A de Sitter no-hair theorem for 3+1d cosmologies with isometry group forming 2-dimensional orbits

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