So we have abandoned this: "This initial state is not at all a point, but the same infinite universe. Quite homogeneous, but nonetheless not exactly homogeneous, but locally inhomogeneous in the same way as our universe today. " Good. Progress.
No reason. I see I was slightly inaccurate in my response. Of course, a sphere is also an infinite set of points. It has a finite volume, but the point was not about the volume. The point was that this is not "nothing", or, say, a single point (the singularity), which would be something one reasonably could name, metaphorically, "nothing".
Next: And you know that it would be a spatial sphere, a three dimensional one, how? Talking below Planck length, we are.
This is what the GR solution for the homogeneous universe tells me. In your beloved case of positive curvature, of course. We have nothing but classical GR, given that quantum gravity we do not have yet. Inhomogeneities I have already mentioned. Wild speculations about topological foam in quantum gravity are irrelevant in the context.
And, anyway, such an even more complex topological foam would be remember "nothing" even less.
So your assertion here: "It does not matter if you cut at Planck time or at 10−1000101000 Planck time, at any particular moment of cutting time the border where you cut is the same full three-dimensional universe" involves a slew of assumptions. I asked why you think other people should make them.
Because we have nothing better. This is what follows from the - according to the mainstream - best available theory, which is classical GR, combined with QFT on curved background. What I have criticized - a "universe from nothing" - is claimed to be based on established science, not? If you, instead, want to discuss a "universe from nothing" based on string theory, astrology or intelligent design, do it, but this would be irrelevant here.
Is it OK if other people want to think about what happened before that arbitrary cut?
Of course. As long as they do not claim that their thinking is based on established scientific theories.
Especially since you have to make the cut after at least part of the separation of forces, before which the "inhomogeneous" nature of the universe is not well defined. That is a measurable, finite amount of time after the bang.
I don't understand what you mean. The evolution equations of GR as well as of QFT on curved background tell me that if the start is homogeneous, it remains homogeneous. Once the result, the world today, is not homogeneous, the early cut cannot be homogeneous too.
About the Holocaust denier defamation:
You state that its nature and significance have not been reliably established according to the evidence you have seen, and that you have good reason to doubt the ordinary, standard history of it.
Not exactly. What I state is that that I have not studied this, so that I cannot make reliable claims about this. I state that I see strong political pressure on those who doubt the standard history, up to imprisonment of revisionists. Strong political pressure on scientists is for me, in general, sufficient reason not to accept the mainstream position in this science without further detailed investigations.
I doubt the reliability of mainstream science in this particular question, because of the obvious political pressure on revisionists, but not their specific claims about the facts.
Your assertion that you would have to do a lot of work to find reliable, as opposed to unreliable, information about the Holocaust is false.
No. We have different standards about what is reliable. You may accept some sources as reliable which I do not accept as reliable. Evaluation of reliability is quite difficult, and a personal decision. If one evaluates scientific papers written under political pressure, the job to evaluate the reliability is an extremely difficult one.
Your claim that the information easily available to you is unreliable is called "casting doubt".
No. Casting doubt means questioning the content of the claim. Considering a particular source as unreliable means questioning the quality of the source of the claim. If the claim is correct or not remains unquestioned.
It may be possible that everyday English is sloppy about this difference. So that sometimes it means this, sometimes that. But there is an important difference between these two things. "Casting doubts" obviously suggests that I do something what I do not, namely to express explicit doubt about particular statements of fact, like that the Holocaust has happened.
Your explanation for your assessment of unreliability - that some countries punish such doubt, so their official histories are dubious - is silly, given that so many other histories are just as easily available as those are, with no more work for you than they involve, and nobody is forcing you to attend only the unreliable sources.
You may not like my criteria for reliability of sources. Feel free to name them silly. Your choice. Assessment of reliability is a difficult personal decision. Moreover, you have not described my criteria correctly. As I have explained, imprisonment is only an extremal case of political pressure. Much less rigorous political pressure is sufficient to distort scientific freedom in such a way that it would be stupid to accept the mainstream without studying the details.
Examples of sciences with much less political pressure, where I nonetheless do not accept the mainstream position without checking it, we have already had: climate change and child labor economics.