Big Bang, Blowup, and Modular Curves: Algebraic Geometry in Cosmology
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
Big Bang, Blowup, and Modular Curves: Algebraic Geometry in Cosmology
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| Creator |
Manin, Y.I.
Marcolli, M. |
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| Description |
We introduce some algebraic geometric models in cosmology related to the ''boundaries'' of space-time: Big Bang, Mixmaster Universe, Penrose's crossovers between aeons. We suggest to model the kinematics of Big Bang using the algebraic geometric (or analytic) blow up of a point x. This creates a boundary which consists of the projective space of tangent directions to x and possibly of the light cone of x. We argue that time on the boundary undergoes the Wick rotation and becomes purely imaginary. The Mixmaster (Bianchi IX) model of the early history of the universe is neatly explained in this picture by postulating that the reverse Wick rotation follows a hyperbolic geodesic connecting imaginary time axis to the real one. Penrose's idea to see the Big Bang as a sign of crossover from ''the end of previous aeon'' of the expanding and cooling Universe to the ''beginning of the next aeon'' is interpreted as an identification of a natural boundary of Minkowski space at infinity with the Big Bang boundary.
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| Date |
2019-02-10T10:10:16Z
2019-02-10T10:10:16Z 2014 |
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| Type |
Article
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| Identifier |
Big Bang, Blowup, and Modular Curves: Algebraic Geometry in Cosmology / Y.I. Manin, M. Marcolli // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 50 назв. — англ.
1815-0659 2010 Mathematics Subject Classification: 85A40; 14N05; 14G35 DOI:10.3842/SIGMA.2014.073 http://dspace.nbuv.gov.ua/handle/123456789/146619 |
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| Language |
en
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| Relation |
Symmetry, Integrability and Geometry: Methods and Applications
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| Publisher |
Інститут математики НАН України
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