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Inference. We can use observation to infer things we cannot directly observe, just as you can infer that the Earth is larger than the visible horizon.
What have you observed that would lead to the inference, since it isn't part of our "observable" universe?????
For example, we observe that the most distant light appears to be 13.8 billion years old, and we also observe that the universe has been expanding since that time. Therefore we can infer that those galaxies must now be much further away - estimates suggest at least 46.5 billion light-years, which makes the universe a minimum 93 billion light-years across, without assuming space beyond the observable universe.
Which in no way infers there must be other universes.... just that this one is larger in extent than you thought.....
And? Since those galaxies must be further than observed, the fact it must be larger is logical....... Which again, does not imply multiple universes.....There are other ways of estimating what's out there, such as the curvature of spacetime; GR suggests that it can be positively curved, negatively curved, or flat. Only the first option would imply a closed, spatially finite universe. A number of different observations suggest that the topology of our universe is flat to a precision of 0.25%, which implies it could be spatially infinite - but if it was not infinite, it would have to be at least 250 times bigger than the observable volume (or we'd measure a greater curvature). This makes it at least 23 trillion light years across, containing at least 15 million volumes the size of the observable universe ('Hubble volume'). 15 million isolated Hubble volumes makes it a minimal candidate for a cosmological multiverse.
Gosh, we wouldn't want to be highly speculative on top of our highly speculative speculations.... But multiverses is of course not highly speculative.... just origins that might contradict the BB....There are also arguments that imply the universe may be significantly larger, but these depend on hypotheses about the causes of the big bang, e.g. inflation theory, that are somewhat speculative.
The observable universe is also much larger than we thought in another sense - the number of galaxies. The Hubble Ultra Deep Field suggested estimates of around 200 billion galaxies, but more recent studies based on Hubble data put it at at least 10 times more than that, i.e. two trillion galaxies; again without assuming space beyond the observable volume.
And some of the furthest are fully evolved, defying the timeframe of the BB.... So perhaps it is infinite and your limit of observation merely limits your view.....
I grew up before Hubble and remember being taught it was only 8 billion lightyears across... Now its 13.7 and yet despite getting bigger, their underlying theory never seems to change, even when the observations falsify the time involved....
After all, before Hubble the universe was theorized to be a lot smaller. I'm waiting on the James Webb telescope so we can see further fully formed galaxies and destroy theory even more..... it's time the Big Bang went Bang and we got a new paradigm that fits reality....
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