Cosmologists tell us that, comparing a subset of models to available data using Bayesian methods, the 14 billion year old universe is somewhere between 3,500,000,000,000 and an infinite number of light years across (emphases mine) ....This is Occam's razor statistics - "... we should tend towards simpler theories .... until we can trade some simplicity for increased explanatory power".
Cosmos At Least 250x Bigger Than Visible Universe - Technology Review
... the photons in the cosmic microwave background have travelled ... 45 billion light years to get here. That makes the visible universe some 90 billion light years across.
... one line of thinking is that if the universe expanded at the speed of light during inflation, then it ought to be 10^23 times bigger than the visible universe... .... Other estimates depend on a number factors and in particular on the curvature of the Universe: whether it is closed, like a sphere, flat or open. In the latter two cases, the Universe must be infinite.
... in recent years, astronomers have various ingenious ways of measuring the curvature of the Universe. One is to search for a distant object of known size and measure how big it looks. If it's bigger than it ought to be, the Universe is closed; if it's the right size, the universe is flat and if it's smaller, the Universe is open.
Astronomers know of one type of object that fits the bill: waves in the early universe that became frozen in the cosmic microwave background. They can measure the size of these waves, called baryonic acoustic oscillations, using space observatories such as WMAP.
There are also other indicators, such as the luminosity of type 1A supernovas in distant galaxies.
But when cosmologists examine all this data, different models of the Universe give different answers to the question of its curvature and size. Which to choose?
The breakthrough that Vardanyan and pals have made is to find a way to average the results of all the data in the simplest possible way. The technique they use is called Bayesian model averaging ...
... Instead of asking how well the model fits the data, its asks a different question: given the data, how likely is the model to be correct. This approach is automatically biased against complex models--it's a kind of statistical Occam's razor.
In applying it to various cosmological models of the universe, Vardanyan and co are able to place important constraints on the curvature and size of the Universe. In fact, it turns out that their constraints are much stricter than is possible with other approaches.
They say that the curvature of the Universe is tightly constrained around 0. In other words, the most likely model is that the Universe is flat. A flat Universe would also be infinite and their calculations are consistent with this too. These show that the Universe is at least 250 times bigger than the Hubble volume. (The Hubble volume is similar to the size of the observable universe.) ...
Given the available information, the universe is most likely infinite, but it could be as "small" as 3,500,000,000,000 light years across. Big enough for one human like civilization for every human that has ever lived.
Probably though, much bigger than that.
It is a bit much. Surely, there is a simpler, less extravagant explanation. I'd like to see the authors rerun their analysis with a broader range of explanatory models. I think I know what the answer would be  ...
See also (Gordon's Notes unless otherwise noted)
- Earth: the measure of all things (3/2007): Back then we thought the universe might be "only" 140 light years across. So Earth was midway between the Planck length (quantum foam scale) and the universe.
- Bayes theorem: binding reasoning to the physical universe (5/2007)
- Boltzmann's brain hits the big Times (1/2008): We are the dreams of a desperate god in a terrible universe. It is the simplest explanation ...
- Reality, perception, Hume, the red pill - and John Tierney (8/2007): If you're going to be crazy like me, it helps to have David Humen for company.
- CV is hurting my head again: The anthropic principle and our peculiar relation to the arrow of time ... (8/2007): Too many coincidences
- The Algebraist and the religion of the eternal simulation (1/2008): Iain Banks is a fabulous writer.
- Ten cosmologies and Theory 10 (8/2006): The original page is gone. You can guess what theory 10 is.
- SETI, the Fermi Paradox and The Singularity: Why our search for extraterrestial intelligence has failed (footnote 9) (@2003) Before I did blogging, I stuck these things in web pages. "... Vernor Vinge wrote a very short story for one of the millenial year issues of either Nature or Science where he explores exactly this premise ... It's interesting to think about how one would "detect" a simulation ... Vinge explored this in a 2004? short story about a woman who realizes she's been trapped in a simulation ... the simulation would be imperfect, that it would generate "artifacts" in the same sense that JPEG lossy compression of a stripped image will product artifacts. One might, for example, look for physical phenomena consistent with techniques that would reduce the computational demands of the simulation. Or one might attempt to expose flaws (bugs) in the simulation -- or even "crash" it (risky!) ... identify physical phenomena that are inexplicable except in the context of a "simulation" (such as "connectedness" in theoretically disconnected parts of the universe).
- Gordon's Notes: Are You Living in a Computer Simulation? (11/04 - one of my earliest posts in this particular thread)
- fn --
 An omniscient universe-creating deity is equivalent to the "Boltzmann's Brain" explanation, so creationists are in good company. Alas, this "deity" is not the one they're looking for.