How Do Critical Density and CMB Irregularities Explain the Universe's Shape?

[leatherneckpa]

I am attending an online college with virtually no contact with peers or professors. Accreditation and scheduling make it the best choice for me. However, I find that I deeply miss the ability to discuss concepts and bounce ideas off p&p. Hence, I find myself here in the hope that I can find answers explained in simple enough terms for a 50+ freshman.

My current problem is trying to wrap my head around the relationship between critical density of the early universe, the modern universe, and the shape of the universe. Hubble's res-shifting, the presence of the CMB, and the composition of old stars were relatively straight forward. But now it's time to incorporate critical density and irregularities in the CMB into some sort of explanation of why the universe is supposed to be flat, and I think perhaps I am hung up on the balloon analogy thing. Or maybe I'm incorporating unrelated thoughts that are unnecessarily muddying the waters.

I keep wondering;

To a paramecium, the palm of our hand would seem infinite and flat. Since we can't see anything beyond 14b years how can we be so certain of the beginning of our universe? Maybe it's just that this is all we can actually see of what is in reality a huge sphere that resulted from the creation of an even larger universe than we imagine. And maybe that started over 100b years ago?​

Can someone attempt to explain to me, in simple terms how critical density and CMB irregularities disprove my unorthodox thoughts?

 

[marcus]

A fundamental cause of a lot of misunderstanding is the unfamiliar transition between verbal/intuitive thinking and mathematical science.

In a mathematical science the focus is on a math model. In cosmology the focus is on math models of the universe: equation models and also massive computer simulations called numerical models. The models must normally be derived from or consistent with the well-tested theory of gravity GR, although some people try out slight modifications.

Basically cosmologists want the simplest equation with the best fit to the data. They have millions of data points. Survey counts of all the galaxies at each distance, and the types, and the organization into clusters... The temperature of the microwave background pixel by pixel. They extract patterns, like the spatial frequencies of fluctuations. How much little ripple versus bigscale fluctuation. They extract structure and the evolutionary history of structure.
So there is this huge body of data.

IT JUST TURNS OUT THAT when you extract the curvature parameter, by taking the best best fit to the data, you get something within one percent of zero curvature.

The uncertainty interval is not exactly centered on zero, but that doesn't count. The point is that if you plug in zero curvature you get the simplest most convenient model to use, and the fit is not any worse than if you plug in 0.001. Or 0.005 or 0.010 or -0.001 or -0.005...

If your paramecium is a mathematical physicist, he will say that for all practical purposes, operationally speaking, the hand is flat. Because that gives him a satisfactory fit and a simple model that works. He is not interested in philosophical questions. He wants to make measurements and make predictions and calculate parameters and get on with business.

However that brings the idea of INFINITE in. I find it more comfortable to imagine a universe with very slight positive curvature so that it is a hypersphere (3D analog of balloon) and therefore has finite volume. I find infinite volume mentally uncomfortable.

But the choice of any number besides zero seems embarrassingly arbitrary. So far the data is not good enough to distinguish between the various positive curvatures close to zero which are in the 95% confidence interval. So I suck it in and say it's flat, along with the other paramecia.

That's how it looks to me. Other people may say different.

 

[Ich]

As marcus said, there's the math model, and there's reality. The math model assumes constant curvature throughout the universe. That could be a very very large hypersphere, or infinite flat or hyperbolic space.
Even then, there could also be notrivial topologies, like flat but finite space.
If you drop the constant curvature assumption, the universe could have whatever bizarre shape, as long as it's nearly flat in our "vicinity".

Now, the inflation model (which is standard, btw) says: whatever the "real" large-scale shape of the universe, whatever its origins, whenever its "real" beginning, it doesn't matter. It will be very close to flat to us paramecia, because there's been something physically going on that ironed it severely.

So your "unorthodox" views can't be disproved. Maybe that's what really happened.
But it doesn't matter, as long as we can neither prove or disprove it, and as long as the standard math model gives the right answers.