Would a Universe without any matter in it, be a singularity?
we have no evidence that spacetime singularities exist, except in the context of certain theories
by definition a singularity is not something in nature, it is a place where some theory breaks down, fails to compute meaningful numbers
historically the way that has be used to eliminate singularities is to improve the theory
several proposed replacements for vintage 1915 GR-based cosmology DO in fact remove the big bang singularity and extend further back in time---this is work in progress
So since as a general rule a singularity is not a physical reality, in any known case, it doesnt make sense to ask the question would a Universe without matter be a singularity. Would ANYTHING really ever be a singularity? I wouldn't know. Since they appear not to occur in nature, probably not.
But there is an easy answer to your question that has nothing to do with singularities.
The de Sitter is an example of a universe with no matter in it. It has a positive cosmological constant. No ordinary matter or dark matter. It has no singularities. (no points at which the model blows up) Just a smooth bounce. Like a big balloon that gradually gets smaller until it reaches some pre-arranged size and then starts expanding again. The minimal size it reaches doesnt have to be especailly small---can still be billions of lighyears in circumference---depends on what parameters you put in the model.
de Sitter is considered a good approximation to our own universe in late times, when matter will have thinned out a lot due to expansion, so the effect of matter will be small and our own universe will behave very much like de Sitter.
the de Sitter model universe was discovered by a dutchman around 1917, as I recall.
there was just a great Scientific American article about it
see "my favorite SciAm article" link in the signature.
But at the moment of the BigBang, there was no matter, just energy, and wasn't that a singularity? As far as I understand it, that's what Stephen Hawking proved.
The field has changed a lot since Hawking was one of the leaders, back in 1970s and 1980s.
No one (not even Stephen H ) has proven that at the moment of the big bang there was actually a singularity! (whether there was or not depends on what model of the big bang you use.)
There are several models of conditions right around the big bang, and in one (the old one based on Gen Rel) there is a singularity at that moment, in other words the model breaks down and quits computing. It is useless trying to describe conditions with a model that has blown up.
With some other models of conditions right around the big bang (before and after the start of expansion) there is NOT a singularity because the models do not break down. what there is generally speaking is very very hot and dense conditions. it would not be too meaningful to try to distinguish between matter and energy in such extreme conditions.
but things still do not go down to a single point---or anything fantastic like that. time doesn't stop existing etc etc.
For example in one bunch of models there is a collapse that leads to the very hot dense conditions and quantum effects cause gravity to be repellent at extreme density and the collapse bounces back and becomes an expansion-----I am trying to tell in words the result of some computer simulation and it is not as good as looking at the graphic plots.
BTW some of Hawking's ideas were still pretty influential in the 1990s. But there has been an enormous change in cosmology since 2000.
There are other people nowadays who are more influential than Hawking in quantum cosmology. One thing you could do is read some and catch up.
There is a new book coming out called Beyond the Big Bang edited by Rudi Vaas. You might look at a copy in the library when it comes out. It is a collection of chapters written by the leading experts. The editor tried to include all the main models---even some older ones that nobody much is currently working on.
Well,.. You´re right that I don't know a lot about these things,. :) Reading up I try, but it's not always that easy. Stephen Hawking is pretty good at explaining stuff in a way that you can (at least feel like you can) understand all this stuff a little bit.
Actually I'm liking this idea of the moment of the big bang not being a singularity. It fits the way I see things. Though I believe it was pretty close to being a singularity, but just not yet. Things nearing infinity, but not reaching it.
By the way, it's interesting how politics and opinions are so important in science,.. :)
Added: Cool stuff in your sig. I'll be spending some time reading that stuff. Thanks!
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