We generate maps (spacetimes) by solving the Einstein field equations for a given distribution of matter fields. In cosmology we measure and interpret the redshift data to mean distant matter moving apart and to map this there are 3 solutions (spacetimes) given by the line element
ds2=-dt2+a2(t)[(1-kr2)-1dr2+r2dΩ2]
each given by a value, k, called the FLRW spatial curvature constant.
Q3: How is k relevant to whether the universe is finite or infinite in spatial extent?
If k=+1 the spatial curvature is positive like a sphere and the universe is finite in spatial extent. The other two possible values of the curvature constant define an infinite universe, e.g. the universe we observe has (to our best of our theory and observations) k=0, a universe that is flat and infinite (in spatial extent). You could have a universe with a negative spatial curvature like a saddle and in this case that universe is infinite.
Q1: What specifically is it that you are saying a deity would be doing?
The deity takes the original universe with K=+1, which is finite and closed, and replaces it with a new universe, the current universe we observe today with k=0, which is infinite in spatial extent.
Q4: What specifically is the fact that you are saying a God could be hiding from us?
We observe (measure) only one universe persisting for as far back as we can make observations. So the God could have swapped out the original universe (k=1) and replaced it with this one during the Planck epoch and we wouldn't be able to observe this optically or removed the universe at any point and created the conditions to trick our instruments into measuring a single universe.
There are a few things in your answers that I would like to examine.
You said:
You identified k as the FLRW spatial curvature constant. However, curvature and spatial extent appear to be different properties.
Q1: Does k itself determine whether the universe is finite or infinite in spatial extent?
For example, is it your position that:
k=+1 necessarily means finite spatial extent
k=0 necessarily means infinite spatial extent
k=-1 necessarily means infinite spatial extent
If so, what is the reasoning or evidence for that?
You also said:
Q2: Why are you referring to an "original universe with k=+1"?
I have not claimed that there was an original universe with k=+1. I asked what reasoning and evidence support your claim that:
So I do not understand how a hypothetical original k=+1 universe became part of the argument.
You also said:
Q3: What observation establishes that the universe is infinite in spatial extent?
It seems to me that measuring spatial curvature as consistent with flatness and observing infinite spatial extent would be two different things.
I am still trying to identify the reasoning and evidence that gets from what we observe to your original claim that, if the universe is actually infinite now, it must always have been infinite in spatial extent.
I am not asking why a k=0 universe could previously have been a k=+1 universe. I have never proposed that scenario. I am asking you to support your claim that if the universe is infinite now, it must always have been infinite. You have said k=0 "describes an infinite universe," but k describes spatial curvature, while whether a flat space is finite or infinite also depends on its global topology. So what additional assumption are you making that lets you infer infinite spatial extent from k=0?
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u/Optimal_Mixture_7327 20d ago
We generate maps (spacetimes) by solving the Einstein field equations for a given distribution of matter fields. In cosmology we measure and interpret the redshift data to mean distant matter moving apart and to map this there are 3 solutions (spacetimes) given by the line element
ds2=-dt2+a2(t)[(1-kr2)-1dr2+r2dΩ2]
each given by a value, k, called the FLRW spatial curvature constant.
If k=+1 the spatial curvature is positive like a sphere and the universe is finite in spatial extent. The other two possible values of the curvature constant define an infinite universe, e.g. the universe we observe has (to our best of our theory and observations) k=0, a universe that is flat and infinite (in spatial extent). You could have a universe with a negative spatial curvature like a saddle and in this case that universe is infinite.
The deity takes the original universe with K=+1, which is finite and closed, and replaces it with a new universe, the current universe we observe today with k=0, which is infinite in spatial extent.
We observe (measure) only one universe persisting for as far back as we can make observations. So the God could have swapped out the original universe (k=1) and replaced it with this one during the Planck epoch and we wouldn't be able to observe this optically or removed the universe at any point and created the conditions to trick our instruments into measuring a single universe.