I Describing the Big Bang

[.Scott]

TL;DR Summary

It started with a point-like singularity? Really?

I started reading a National Geographic article related to the Big Bang. It starts these statements:

Gazing up at the stars at night, it’s easy to imagine that space goes on forever. But cosmologists know that the universe actually has limits. First, their best models indicate that space and time had a beginning, a subatomic point called a singularity. This point of intense heat and density rapidly ballooned outward.

My first reaction was that this is a layman's approximation to the actual Physics view.
My second reaction was "What IS the actual Physics view?".

This singularity can't be a "point" because there is no such Physical thing. The amount of information you can store in an object of true zero diameter is zero. And if you make it 10-dimensional, it's still zero.

So, perhaps it was a fuzzy point.

And then it inflated (wiki article). That wiki article cites a standard college text book in describing it this way:

All of the mass-energy in all of the galaxies currently visible started in a sphere with a radius around 4 x 10-29 m then grew to a sphere with a radius around 0.9 m by the end of inflation

Per Wiki's "Shape of the Universe" (citing NASA sources):

Current observational evidence (WMAP, BOOMERanG, and Planck for example) imply that the observable universe is spatially flat to within a 0.4% margin of error of the curvature density parameter with an unknown global topology.

So we have "currently visible", "sphere", and not much curvature.
And the "sphere" we are talking about is the volume interior of a 3-D sphere. You can recast it as the surface of a 4-D sphere, but I don't believe Big Bang was suppose to posit a particular topology for our universe.

So, perhaps the problem is simply with "sphere". Perhaps when I hear "sphere", I should replace it with "some finite topology" - it could be a Klein bottle. So we have a fuzzy point, puffs up to some topology (perhaps a Klein bottle or Sphere) which includes our visible universe ... but probably some regions that are not visible. How could it exclude our geometric neighbors. So that "singularity" included, not just everything in the "visible universe", but everything in some finite topology. Sure, why not? Our fuzzy little point probably just got a bit bigger, but why not?

But presuming a finite topology when our best measurements say that it's flat to within an 0.4% margin is being pretty presumptuous. What happens if we try a flat 3D "plane" of infinite extent? Well that fuzzy point just turned into a flat 3D "plane" as well. After all, the Big Bang inflation was just a initial finite dimension multiplied by a constant. If the result is an infinite length, then the initial dimension must have been infinite as well.

Anyway, at this rate, I will never finish that National Geographics article.