Nardelli, Michele (2009) On some mathematical connections between the Cyclic Universe, Inflationary Universe, padic Inflation, padic cosmology and various sectors of Number Theory. Dip.Sc.TerraDip.Matem.Unina. (Unpublished)

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Abstract
This paper is a review, a thesis, of some interesting results that has been obtained in various researches concerning the “brane collisions in string and Mtheory” (Cyclic Universe), padic inflation and padic cosmology. In the Section 1 we have described some equations concerning cosmic evolution in a Cyclic Universe. In the Section 2, we have described some equations concerning the cosmological perturbations in a Big Crunch/Big Bang spacetime, the Mtheory model of a Big Crunch/Big Bang transition and some equations concerning the solution of a braneworld Big Crunch/Big Bang Cosmology. In the Section 3, we have described some equations concerning the generatine Ekpyrotic curvature perturbations before the Big Bang, some equations concerning the effective fivedimensional theory of the strongly coupled heterotic string as a gauged version of N = 1 fivedimensional supergravity with fourdimensional boundaries, and some equations concerning the colliding branes and the origin of the Hot Big Bang. In the Section 4, we have described some equations regarding the “null energy condition” violation concerning the inflationary models and some equations concerning the evolution to a smooth universe in an ekpyrotic contracting phase with w > 1. In the Section 5, we have described some equations concerning the approximate inflationary solutions rolling away from the unstable maximum of padic string theory. In the Section 6, we have described various equations concerning the padic minisuperspace model, zeta strings, zeta nonlocal scalar fields and padic and adelic quantum cosmology. In the Section 7, we have showed various and interesting mathematical connections between some equations concerning the padic Inflation, the padic quantum cosmology, the zeta strings and the brane collisions in string and Mtheory. Furthermore, in each section, we have showed the mathematical connections with various sectors of Number Theory, principally the Ramanujan’s modular equations, the Aurea Ratio and the Fibonacci’s numbers.
Item Type:  Article 

Subjects:  500 Scienze naturali e Matematica > 510 Matematica 
Depositing User:  Michele Nardelli 
Date Deposited:  05 Feb 2009 
Last Modified:  20 May 2010 12:01 
URI:  http://eprints.bice.rm.cnr.it/id/eprint/736 
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