Size of universe and quantity of mass

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The discussion centers on the possibility of an infinite universe containing a finite amount of mass and energy, with the remainder being empty space. While there is no definitive reason provided against this idea, it contrasts with the prevailing belief that the universe is homogeneous and isotropic on large scales. Evidence from observations supports the notion of uniformity in the universe's structure. The implications of an infinite universe with finite mass challenge current cosmological models. Overall, the conversation highlights the complexities of understanding the universe's size and composition.
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If the universe is infinite in size, is possible that it only have a finite amount of mass/energy with the rest of the universe being completely empty?
 
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I can't think of a precise reason why it's impossible, but it's generally believed that the universe is the same everywhere (averaged over appropriately large scales), and there is good evidence that this is true in our observational universe.
 

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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