Cosmos Theory has a sequence of 10 spaces. Ten spaces are Physical in the sense of supporting universes. Previously, we found sequences of Coupling Constants, of up-type fermion masses, and of down-type fermion masses. We now extend Cosmos Theory to sequences of universe masses at the time of universe creation and to the Gravitation constant G.
This book covers many topics. It considers these topics from a deeper perspective in Mathematics and Geometry. The book suggests fermions have inner universes that explain their masses.
The sequence of Cosmos spaces is the result of the number of totally antisymmetric tensors of dimension r and the number of creation and annihilation operators in a Fermion wave function - Mathematics!
Coupling constants form a sequence in powers of two - they are a product of the number of fermion spins in a symmetry group representation - Mathematics and Geometry - based on a product of degrees of freedom and multi-dimensional geometry volume and surface values.
The two sequences of fermion masses that the author found are the result of an internal universe shell for each fundamental fermion. Up-type fermions have 5, 4, 3, and 2 dimension internal universe shells. Down-type fermions have 3 dimension internal universe shells. The shells generate powers of pi = 3.14159 and e = 2.718 Geometrically.
They implement the mass multipliers:
Up type fermion multiplier: 32 pi
Down type fermion multiplier: 32
The 32 multiplier appearing in both sequences is the number of Normal (non-Dark) fermions in a fermion layer.
The appearances of e and pi are explained as due to volume and surface factors in the fermion mass based on a universe consistency condition applied for fermion stability - Geometry!
The form of the e and pi mass entries is the reason for viewing fermions as having internal universe shells based on their variations. These pi and e variations, based on internal universe shell dimension, are "explained" by volume and surface area factors - Geometry!
The sequence of universe total mass-energies E is based on a universe creation consistency condition - a consistency condition for the creation of a universe where the pressure in the universe equals the Casimir force generated by the enclosing universe. The total mass-energy has a joint sequence in powers of 2, of the enclosing universe's dimension, and of the universe's dimension r. The basis of its form is the form of surface area and volume in various dimensions, and of Cosmos Theory dimension array sizes (numbers of fermions).
These results suggest that a universe is a form of particle.
The gravitation coupling constant G is associated with the SU(256) symmetry group. A mass factor is required on dimensional grounds in gravitational dynamic equations. This factor causes gravitation G to be weak. We now have a viable estimate of the value of G and its origin in a coupling constant formulation.
The seven sequences that appear: Cosmos spaces, Coupling Constants, Gravitation coupling constant, Up-Type fermions, Down-Type fermions, Vector Boson W and Z masses, and universe masses are all based on Mathematics and Geometry.
We conclude the total Lagrangian for our universe is significantly fixed:
1. Cosmos Theory gives spaces and dimension arrays, coupling constants and masses.
2. The particle Lagrangian is almost totally defined by using coupling constants and masses (and scalar and vector bosons).
A fait Accompli!
The book's list of evidence for Cosmos Theory is further augmented by the calculation of the Weinberg angle and the vector boson Z and W masses. The book also makes projections of fermion masses to as yet unknown higher generations.
