I Big Bang singularity: can we say anything about its size?

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The discussion centers on the nature of the Big Bang singularity, questioning whether it can be defined as finite or infinite. It suggests that if the singularity is infinite, then the Universe must have always been infinite, complicating the concept of transition from finite to infinite post-Big Bang. The role of cosmological inflation is examined, raising questions about whether the Universe's expansion pertains to volume or spatial dimensions. The conversation references insights from articles on the Big Bang, indicating a need for further exploration of these concepts. Overall, the dialogue emphasizes the complexities surrounding the definitions and implications of the singularity in cosmology.
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Has the Universe been anything other than infinite? (ie finite)
The Big Bang is sometimes described as started from a singularity, which I have interpreted as meaning that its characteristics are undefineḍ. If that is the case, can we not even say that the Universe as a singularity was still infinite? Otherwise we are implying that the singularity was finite, and at some point after the Big Bang, there must have been a point in time when there was a transition from finite to infinite.

Cosmological inflation suggests that the Universe is expanding. Is this by volume? That doesn't make sense to me. If the Universe is infinite in volume, at no point during the inflationary period could it have been anything less than infinite? Or does this suggest that spatial expansion is not related to volume?
 
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Thread 'Matter density right after the decoupling'

https://en.wikipedia.org/wiki/Recombination_(cosmology) Was a matter density right after the decoupling low enough to consider the vacuum as the actual vacuum, and not the medium through which the light propagates with the speed lower than ##({\epsilon_0\mu_0})^{-1/2}##? I'm asking this in context of the calculation of the observable universe radius, where the time integral of the inverse of the scale factor is multiplied by the constant speed of light ##c##.
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Thread 'Rutgers finds a transparent Einstein Cross - apparently a dark matter "halo".'

The formal paper is here. The Rutgers University news has published a story about an image being closely examined at their New Brunswick campus. Here is an excerpt: Computer modeling of the gravitational lens by Keeton and Eid showed that the four visible foreground galaxies causing the gravitational bending couldn’t explain the details of the five-image pattern. Only with the addition of a large, invisible mass, in this case, a dark matter halo, could the model match the observations...
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Thread 'Big Bang and Infinite Universe'

Hi, I’m pretty new to cosmology and I’m trying to get my head around the Big Bang and the potential infinite extent of the universe as a whole. There’s lots of misleading info out there but this forum and a few others have helped me and I just wanted to check I have the right idea. The Big Bang was the creation of space and time. At this instant t=0 space was infinite in size but the scale factor was zero. I’m picturing it (hopefully correctly) like an excel spreadsheet with infinite...
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