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How does the scale of a cataclysm determine if we can look beyond it?

Cataclysmicity is not a physically measurable observable. That part of the quote is not physics. The first sentence should refer to the theories of cosmology, plural possessive. Cosmology is a branch ...
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Writing the metric of 4D de Sitter space as a 5D metric

What you want is the induced metric. I am not going to solve this explicitly for you since this is a very standard homework/exam exercise. But let me sketch the identical computation for a sphere. A ...
Supernovae measurements provide constraints on $\Omega_k$ independent of CMB measurements. A relatively up to date example of this are the constraints from the Pantheon supernovae sample, detail in ...