1. I will try to explain this in another manner. Have you ever squeezed a ball that was filled with air and the air ''pushes'' back? The air wants to permeate more than it can but is ''squeezed'' together. Now think about the field line, the density would certainly permeate more if it were not for the likewise opposing force of ''itself''.
2. I do not know the maths at this time.
3. By defining it in an abstract manner. (I will think harder about this question).
p.s Field lines want to be a sphere but they can't by there own mechanism.
They may form by a fractal function. See Causal Dynamical Triangulation (CDT)
Causal dynamical triangulation
Causal dynamical triangulation (abbreviated as CDT) invented by Renate Loll, Jan Ambjørn and Jerzy Jurkiewicz, and popularized by Fotini Markopoulou and Lee Smolin, is an approach to quantum gravity that like loop quantum gravity is background independent.
Causal dynamical triangulation - Wikipedia
https://
en.wikipedia.org/wiki/
Causal_dynamical_triangulation
Edit: It seems to me that if there was an underlining field such as the Higg's field, then this field must be neutral?
I may have read that all particles in the Higgs field may be entangled. If the Higgs boson is the glue in forming matter, is it not logical that all Higgs bosons are glued to themselves (entangled)
As I understand it, the real mystery lies in the question what was causal to the BB, and if that event might have been causal to the universal soup of bosons, such as the Higgs field.
a) Energy always existed but dispersed through a near infinite vacuum. (unlikely?)
b) Energy was created during the BB, by an unknown event. (possibly?)
If I may be permitted a pure speculation. A flight of fancy.
Comes to mind if a near infinite timeless vacuum were to instantly totally collapse into itself, creating a singularity and though a vacuum itself may not have any physical properties, when a near infinity of nothing is reduced (compressed) into a singularity, is it possible that the collapse itself might produce an energetic rebound, creating bosons in the process (inflationary epoch)?
There has to be a logical if not mathematical causality for the BB. Strange as it may be to our current understanding of the physical universe, I doubt that it was created by magic.
I find it highly unlikely that some form of energy always existed. IMO, energy was created by an event.
So if we begin with the assumption of the existence of a near infinity of pure nothingness, how can nothingness be brought to produce an energetic event. If nothingness = pure vacuum, would there exist a natural imperative (a potential) that it must collapse unto itself? If that riddle could be solved, might it lead to a logical answer of "in the beginning"
In a timeless pre-condition, this event would be instantaneous and might produce a mega quantum event, creating a virtual Higgs field and the subsequent assembly of primary particles.
I'm in deep, deep water here, but hey if the pre-condition to the BB is still a mystery, perhaps a flight of fancy might provide a creative spark in the mind of a knowledgeable fellow.