A cubic lightyear is about 8.468e+50 liters, and butter weighs 911 g/L, giving the mass of a cubic lightyear of butter to be 7.714348e+50, whose Schwarzchild radius is about 121,103,293 lightyears, about 100x smaller than the radius of the known universe.
... maybe it is? Hear my pet theory out.
Extrapolating backwards from the expansion of our universe, the Big Bang model posits a hyperdense state that exceeds black hole levels originating from a singularity, yet it's thought that somehow it did not collapse back, handwaving it as "physics as we know it did not apply".
But maybe physics as we know it does apply. Notably physics as we know it does not imply a specific direction for the arrow of time.
So our universe might very well be a black hole, but we have time backwards compared to the usual way we think of black holes: what we think of as the origin of time and space is what we think of as the irremediable end of time and space in a black hole.
radius of universe = 4.4 * 10^23 km (47b ly)
mass required to have schwarzschild radius of 4.4 * 10^23 km = 2.96 * 10^53 kg
Surely we are still discovering the implications of these numbers being so close.
I like your time-reversed black hole framing, thanks for that.
https://www.wolframalpha.com/input?i2d=true&i=+schwarzschild +radius+of+mass+of+the+universe
https://www.wolframalpha.com/input?i=radius+of+universe
https://www.wolframalpha.com/input?i2d=true&i=+schwarzschild +radius+of+2.96*Power%5B10%2C53%5D+kg
Before ANGRY KEYBOARD SOUNDS commence, I'm not saying we don't know what mass is, I'm saying fundamentals. I.e., why is mass. What causes it to come into being? Bulk entanglement, i.e., a function of probability or "mass as destiny"? Tiny signals? Lots of rubber sheeting? Etc.
Ok.
> a black hole, but we have time backwards compared to the usual way we think of black holes
Observations of our universe are straightforwardly understood -- and predicted -- by laying matter fields on an expanding Robertson-Walker metric. The same observations are not at all easy to understand by laying matter fields on a time-reversed Oppenheimer-Snyder-like black hole metric.
The first thing you run into is that at the largest scales (i.e., where the solid angles subtended by galaxy clusters are small for observers like us) visible matter is arranged roughly isotropically and roughly homogeneously: we detect typical spiral galaxies (and more importantly various atomic line transitions associated with them, like the <https://en.wikipedia.org/wiki/Lyman-alpha_forest>) at all sorts of redshifts.
Your homework would be to generate lightlike geodesics that can reproduce these observations at any time in a black-hole-like metric. If you can do that at for a single spacelike slice of your black hole, you then would want to work on evolving that slice using e.g. the <https://en.wikipedia.org/wiki/Initial_value_formulation_(gen...>.
Just scratching the surface of how you would go about doing that would be an interesting research project for a layperson. Among other things, you would end up learning a lot more about what's in your second paragraph, and likely develop an idea about how much work is involved in writing down even a simple "pet theory" of physical cosomology that accords with observational data. Or at least you'd have a better idea of what observational data there is that needs to be accounted for. You'd also confront all sorts of open questions about the interiors of black holes where there is significant matter; that would be timely given the recent preprint by Roy Kerr at <https://arxiv.org/abs/2312.00841>.
Now, since the universe doesn't appear to be a blackhole, we assume there's an equal amount of stuff outside of it pulling it back into flatness.
The hoop conjecture doesn't apply in a small region of a very homogenous universe
The mass of ordinary matter in the universe is 2×10^53 kilograms, which would have a Schwarzchild radius of 31.39 billion light years. The explanation from popular science communicators on this topic have never satisfied me.
Your maths is correct for one cubic light year of butter. Proxima Centauri is 4.247 light years away, and that gives such a cube of water[0] a mass of 6.468×10^52 kilograms[1], which would have a Schwarzchild radius of 10.15 billion light years.
[0] At STP, which isn't realistic at all
[1] Close enough; I think it was Brian Cox who once joked that in cosmology it is standard practice to approximate π as 1.