http://ift.tt/1jrp12J
Big Bang, Blowup, and Modular Curves: Algebraic Geometry in Cosmology
Yuri I. Manin, Matilde Marcolli
(Submitted on 10 Feb 2014 (v1), last revised 9 Jul 2014 (this version, v3))
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. [COLOR="rgb(0, 100, 0)"]We argue that time on the boundary undergoes the Wick rotation and becomes purely imaginary [/COLOR]. 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.
http://ift.tt/1AC4XBo
They suggest a model of the kinematics of Big Bang using the algebraic geometric (or analytic) blow up of a some point creating a projective space boundary of light cone in which time on the boundary undergoes the Wick rotation and becomes purely imaginary by postulating that the reverse Wick rotation follows a hyperbolic geodesic connecting imaginary time axis to the real one.
Well. Math is fun i guess (Exclusive to mathematicians)..
Big Bang, Blowup, and Modular Curves: Algebraic Geometry in Cosmology
Yuri I. Manin, Matilde Marcolli
(Submitted on 10 Feb 2014 (v1), last revised 9 Jul 2014 (this version, v3))
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. [COLOR="rgb(0, 100, 0)"]We argue that time on the boundary undergoes the Wick rotation and becomes purely imaginary [/COLOR]. 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.
http://ift.tt/1AC4XBo
They suggest a model of the kinematics of Big Bang using the algebraic geometric (or analytic) blow up of a some point creating a projective space boundary of light cone in which time on the boundary undergoes the Wick rotation and becomes purely imaginary by postulating that the reverse Wick rotation follows a hyperbolic geodesic connecting imaginary time axis to the real one.
Well. Math is fun i guess (Exclusive to mathematicians)..
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