Kewl, Mr. Einstein^4, you set up a bank shot to put you in the side pocket.<quoted text> You are asking me to measure the immeasurable to justify your belief it can be. The initial expansion from an infinitesimal is theoretical and not actually measurable, since it expanded from every point in space and every point appears to be the initial expansion point. At 10-^37 seconds into the expansion, a phase transition caused *cosmic inflation, during which the universe grew exponentially.
See Space expands
This is just like an inside-out black hole metricit has a zero in the dt component on a fixed radius sphere called the cosmological horizon.
So you see you still have to deal with a cosmological horizon, where beyond this point it's infinite, and we can only measure the observable horizon.
Every point in space? From a singularity?
Let's get real infinitestimal, mathematical, and conceptual.
Remember my hex plotting of points in a plane or volume?
Let's get to the ultimate infinitestimally smallest point. Your starting point for expansion. You can't expand unless you have someplace to start, in the real world, anyhow. We will start on a plane.
Draw a point, Sparky. How many directions can you then proceed in? Well, lets draw the same size points around it. You will get 6. Now you can take a step. Now draw points around that step you took. How many directions can you go now without turning around? Work your way out. Keep in mind that first step started motion. Also keep in mind you can't turn around on a single point. Something about radius and pi. What is pi times an infinitestimally small point and the path width you will have to follow from it?
Now proceed and create your universe by going 3D. Don't forget the 7/8th base of height between the centers of your theoretical smallest points, and thus incremental distance. Plays hell with a continuum. All it takes is paper and pencil and an understanding.