An Approach to the Primordial Universe Using Colombeau's Simplified Algebra
General Relativity and Quantum Cosmology
2023-03-22 v1 Mathematical Physics
Functional Analysis
math.MP
Abstract
The proposal "no boundary" of physicists Hartle and Hawking seeks to build a satisfactory model of the early Universe, in a way that avoids the singularity "Big Bang" of the beginning of the Universe. As a consequence of this proposal, the concept of metric signature change arises, which is approached in different ways in the literature. Here, we reinterpret the Mansouri-Nozari approach, which modifies the FLRW metric, and uses the formalism of Colombeau's Algebras, to develop its equations. In addition, we write the function that changes the sign in terms of redshift. Finally, we developed Friedmann's equations, of the modified metric, as well as the equation of state and other relevant equations in Cosmology.
Keywords
Cite
@article{arxiv.2303.11907,
title = {An Approach to the Primordial Universe Using Colombeau's Simplified Algebra},
author = {Jonatas A. Silva and Fábio C. Carvalho and Antonio R. G. Garcia},
journal= {arXiv preprint arXiv:2303.11907},
year = {2023}
}