Types of quantum field thories
On the very largest scales observable in astrophysical experiment, the cosmos is well described by an FRW model with cosmological constant , with plenty of dark matter and with primordial cosmic inflation (called the -CDM “concordance model of cosmology”). A horizon in there and everything on smaller scales is the observable universe.
There has never been a reason to assume that beyond this cosmic horizon visible to us today, the cosmos would not extend further. In fact in the simple FRW models with positive cosmological constant, the spacetime manifold is not a closed manifold and extends indefinitely beyond our observable horizon. This is directly analogous to the ancient mariner who would stand on the deck of his ship and see a few miles of ocean around him. That was the world within his horizon, but there was no telling what lay beyond.
Therefore it is important to distinguish the observable universe from the universe as such. Unfortunately, intellectual laziness tended to ignore this distinction and at some point some people who said “universe” to mean just the stretch of our cosmic horizon felt the need to have a new term for whatever may lie beyond. For better or worse, that new term has become wide-spread these days and is “multiverse”.
The main scientific observation that goes with this is the observation that cosmic inflation – for which there is by now excellent and ever increasing experimental evidence that indeed it happened – does, at least by the simple method which is currently used to model it, naturally predict a large ambient space in which local regions stochastically undergo inflationary expansion. This scenario of chaotic inflation has in fact been singled out as the most likely one (within the standard model) by the bicep2-experiment in 2014.
In any case, as far as the observable universe is concerned, two facts are worth noticing:
the observable universe alone is already pretty darn large, see the various discussion of its scales below;
Giordano Bruno’s old intuition remains plausible even at the largest scales: possibly the full xyz-verse beyond our present horizon is vastly larger still… and we may never know.
Recent measurements (c. 2001) by a number of ground-based and balloon-based experiments, including MAT/TOCO, Boomerang, Maxima, and DASI, have shown that the brightest spots are about 1 degree across. Thus the universe was known to be flat to within about 15% accuracy prior to the WMAP results. WMAP has confirmed this result with very high accuracy and precision. We now know that the universe is flat with only a 2% margin of error
A visualization of the scales in the solar system are in
A visualization of the big observable structures in the universe, drawn to scale, is in
A simulation of these is at
Survey and exposition of aspects of organizing the large-scale structure of the universe are at
More technical discussion of cosmic horizons contains
A sketch of a comprehensive picture had been proposed in