Try not to think of the universe as embedded in some higher dimensional space. That will lead to all sorts of confusions. For example, if our universe had the shape of a cylinder, that would still be closed but flat (i.e. Eucledian geometry).

You don't have to guess or assume. If you are interested, you can do the calculations yourself and check. Maybe you are right and I'm wrong, but I don't have the energy to do the calculations just for the purpose of a forum post. The calculations are not difficult, they are just very long and tedious, so if you are interested I really invite you to do it yourself.

I'll help you get started: Start with the Robetson-Walker metric:

Friedmann?Lemaître?Robertson?Walker metric - Wikipedia, the free encyclopedia

Use natural units to make the math simpler, so the metric becomes:

ds^2 = - dt^2 + a^2 ( dr^2 / (1 - k r^2) + d theta^2 + r^2 sin(theta)^2 d phi^2 )

Compute the components of the Riemann:

Riemann curvature tensor - Wikipedia, the free encyclopedia

Christoffel symbols - Wikipedia, the free encyclopedia

From here you compute the components of the Ricci tensor and then the Ricci scalar:

Ricci curvature - Wikipedia, the free encyclopedia

The Ricci scalar gives you the curvature. What you want to know is whether it gets very large when t goes to 0.

If you are not practiced doing these calculations it might take you an afternoon, or maybe a day to do them. So you can set aside Saturday and get the answer if it is important to you. Then you can post here the value of the Ricci scalar and we'll see.

But I hope you'll understand if I don't want to do go through all this work just to argue a point in a forum. For one, even if you are right in principle, we'd still have to figure out how small the universe has to be before curvature is significant enough to matter at the scale of nuclear interactions, which is a very small scale. I suspect that what you'll find is that it doesn't matter. I expect you'll find that by the time the universe is cool enough to allow nuclear interactions, it has expanded enough that from the point of view of a quark it might as well be flat.

You cannot claim that because it is a subject you do not understand. You should only make claims that are commensurate with your knowledge. However, you can ask. Asking is always ok.However, I have one point I would want yet to push -- neutrinos. Our cosmos is submerged in a sea of cold neutrinos, a 'neutrino CMB' as it were. Please ponder this point -- 'way back when', there was an ultra-relativistic, ultra-dense 'neutrino fog', through which all the then-fusing baryons were obliged to propagate. Can I not claim, that modern human particle-accelerator experiments do not mimic such 'neutrino-dense' conditions? And, if not, how would such a 'neutrino soup' backdrop, or stage, have affected the physics??

There is (probably) indeed aneutrino background, analogous to the CMB. This is not unknown or unexpected physics. The neutrino background predates nucleosynthesis by a long while. The universe becomestransparent to neutrinos at about the time the quark-gluon plasmacools enough to produce hadrons. This happens several minutes before the universe is cool enough to even allow nuclear fusion. In other words, by the time the universe is cool enough that nuclear fusion is even possible, it is more than cool enough that neutrinos don't affect the interactions.

But anyway, you touch on this subject in your post, so let's just continue and answer your next question:

It is the difference between the strong nuclear force and gravity. You made a mistake by saying "interaction with matter" without thinking deeper about what interactions you are talking about. The features in the CMB are large scale (i.e. cosmic scale) density fluctuations driven by gravity. Neutrinos produce gravity too, and the amount of neutrinos has detectable effects in cosmic structures.I notice that that cited article does say, that the ultra-relativistic, primordial, neutrinos would have cooled out of matter-interactiveness, aftertwo seconds--several minutesbeforeeven PNS. Yet, those same neutrinos, after a further ~400 kyrof cooling, interacted strongly enough with matter, to smooth out fluctuations, ultimately imprinted in the CMBR. I don't understand, how, if neutrinos were matter-interactive, at400 kyr, why they weren't, at4 minutes.

Incidentally, this is one of the reasons why neutrinos are not the most popular candidate for dark matter. Neutrinos move very fast. If they were the bulk of dark matter, they would make it harder for galaxies to form and galaxies would form top-down, while we can observe that galaxies formed bottom-up.

So as you can see, neutrinos can have perfectly valid effects on the large scale structure of the universe, and none of that implies that they affect nuclear fusion. Fusion is not driven by gravity, it is driven by the strong and weak nuclear forces, and it happens on the nuclear length scale, while the CMB shows features in the scale of the universe.