Big Bang, Blowup, and Modular Curves: Algebraic Geometry in Cosmology
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 po...
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| Дата: | 2014 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2014
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/146619 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | 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. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
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irk-123456789-1466192019-02-11T01:23:46Z Big Bang, Blowup, and Modular Curves: Algebraic Geometry in Cosmology Manin, Y.I. Marcolli, M. 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. 2014 Article 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 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| 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. |
| format |
Article |
| author |
Manin, Y.I. Marcolli, M. |
| spellingShingle |
Manin, Y.I. Marcolli, M. Big Bang, Blowup, and Modular Curves: Algebraic Geometry in Cosmology Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Manin, Y.I. Marcolli, M. |
| author_sort |
Manin, Y.I. |
| title |
Big Bang, Blowup, and Modular Curves: Algebraic Geometry in Cosmology |
| title_short |
Big Bang, Blowup, and Modular Curves: Algebraic Geometry in Cosmology |
| title_full |
Big Bang, Blowup, and Modular Curves: Algebraic Geometry in Cosmology |
| title_fullStr |
Big Bang, Blowup, and Modular Curves: Algebraic Geometry in Cosmology |
| title_full_unstemmed |
Big Bang, Blowup, and Modular Curves: Algebraic Geometry in Cosmology |
| title_sort |
big bang, blowup, and modular curves: algebraic geometry in cosmology |
| publisher |
Інститут математики НАН України |
| publishDate |
2014 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/146619 |
| citation_txt |
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. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
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AT maninyi bigbangblowupandmodularcurvesalgebraicgeometryincosmology AT marcollim bigbangblowupandmodularcurvesalgebraicgeometryincosmology |
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2025-07-11T00:20:18Z |
| last_indexed |
2025-07-11T00:20:18Z |
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1837307818664787968 |