Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Big Bang, Blowup, and Modular Curves: Algebraic Geometry in Cosmology

  1. Jul 31, 2014 #1
    http://arxiv.org/abs/1402.2158

    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. 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.



    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)..
     
    Last edited by a moderator: Sep 25, 2014
  2. jcsd
  3. Aug 5, 2014 #2
    I'm sorry you are not generating any responses at the moment. Is there any additional information you can share with us? Any new findings?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Big Bang, Blowup, and Modular Curves: Algebraic Geometry in Cosmology
  1. Before the Big Bang (Replies: 12)

  2. Pre-Big Bang Scenario (Replies: 3)

  3. Holographic big bang (Replies: 1)

Loading...