The answer is no: or at least, the total angular momentum of the universe is zero. The
equations that describe our universe are predicated on the assumption that the universe is
isotropic. That means there is no preferred direction in space. If there was a total angular
momentum for our universe then since this is a vector quantity it would represent a
preferred direction. The fact that these equations accurately reflect the universe we
observe on its largest scale suggests that no such preferred direction exists.
Of course our universe isn't precisely isotropic. There are very, very small
variations in the cosmic microwave background radiation for example, but on the scale of the
overall universe these sorts of things are enough to produce an appreciable angular
momentum.
Answered by: Brent Nelson, M.A. Physics, Ph.D. Student, UC Berkeley
'The strength and weakness of physicists is that we believe in what we can measure. And if we can't measure it, then we say it probably doesn't exist. And that closes us off to an enormous amount of phenomena that we may not be able to measure because they only happened once. For example, the Big Bang. ... That's one reason why they scoffed at higher dimensions for so many years. Now we realize that there's no alternative... '