TITLE:
Examining Toroidal Geometry in Terms of a 3-Dimensional “Tokamak”, and the Use of a Toroidal Universe
AUTHORS:
Andrew Walcott Beckwith
KEYWORDS:
Toroidal Universe, Friedman Geometry, Hubble Parameter, Vacuum Energy Density, Early Universe Entropy
JOURNAL NAME:
Journal of High Energy Physics, Gravitation and Cosmology,
Vol.12 No.2,
April
29,
2026
ABSTRACT: We begin with a review of Friedman geometry in order to get a relationship between vacuum energy density and Hubble expansion parameter. Furthermore, in line with Utpal Sarkar, we can write the Hubble parameter as proportional to the square of background temperature, which is important in our derivational work. Furthermore, in line with work presented by Guth and Vilikin, we can obtain
g
00
=1
for a time component in the Toroidal universe by setting a three dimensional line element as embedded in the square of a scale factor
a(
t
)
times the “line element” given by R. Murdzek (which has a 3 dimensional presentation of a Ricci scale factor). Incorporating the Guth and Vilikin “line element” trick, for a Toroidal universe allows
g
00
=1
for obtaining a non-zero stress energy tensor we can write as
T
00
as a non-zero value even if the Ricci component
R
00
in our construction is zero. We also close with a model of how all this is proportional to low entropy conditions in the early universe, citing a paper done by the author and Lousto et al. who modeled early universe conditions on black hole physics.