The Instantaneous Creation of Infinite Space

OK. So I can type faster than I can think.
Here's my CORRECTION:

The Instantaneous Creation of Infinite Space

The 3-space in which we live is one of an infinite variety of possible
geometries. http://arxiv.org/PS_cache/gr-qc/pdf/9804/9804006.pdf. No
mortal can identify the right spatial form. The Big Bang creation
story comes in two incomprehensible versions. No human knows which
version is correct. This thread is a request that knowledgeable
mathematicians answer questions as simply as possible on the very
essence of mathematical cosmology and what is knowable and provable.

The most delightful creation story is that, in an instant, out of
nothing, infinite space suddenly came to be. The infinite and
everywhere appeared instantly, inexplicably; and time was also born.
The second creation story is a plain and simple alternative to the
first. Space (the everywhere) was born finite, with zero volume and
grew from that; and time also came to be.

The birthing of geometry in time has associated with that space and
time, a flow of idealized, mathematical trajectories. Each trajectory
is easily pictured as the spatial trace of an abstract idealized clock
moving effortlessly through that geometric space, parameterized by its
own clock time. Each clock, therefore, is defined by a timelike
geodesic.

The most glaring fact that I see in the simultaneous emergence of
space and time is the existence of the above mentioned global flow of
abstract coordinate clocks, all initially synchronized by God Himself.
Obviously, attempting mathematical physics by coordinatizing space
and time, if space is infinite and flat, can not produce the Lorentz
transformation. It isn't the Creator's choice. It doesn't harmonize
with creation. Going the route of conventional special relativity
would imply that imagining an event at some time in one frame of
reference would necessarily translate to the same event happening
in another frame before time even began. It's against nature.

Imagine the second creation story and the birthing of a hypersphere
(or projective 3-space if you prefer) from an initial inexplicable
point. The symmetry of this space demands a corresponding symmetry
in the global multidirectional flow of abstract coordinate clocks.
To understand this symmetry physically, I wish to understand motion
generally. My most stubborn and longstanding expectation is that
all motions in spatially compact spacetimes have extremely absolute
characteristics, whereas, all motion in spatially infinite spacetime
is relative.

Therefo I would like to define a geodesic coordinate system in
space as a flow of our abstract idealized clocks such that all those
clocks travel the same distances as a function of clock time. I also
like the requirement that nearby clocks in the flow all move in
approximately the same direction. What are all the global geodesic
coordinate systems for an expanding circle, sphere and hypersphere?

Eugene Shubert
http://www.everythingimportant.org