The "big crunch" wikipedia says that it's an idea about the end of the universe, where expansion will reverse and everything will collapse back in on itself.
That is not what I'm asking. I'm asking if expansion and contraction could fluctuate in perpetuity, like stress waves through a block of jello.
We believe that the universe is accurately described by the Friedman-Lemaitre-Robertson-Walker metric, for which we have good reasons, and which only allows a few trajectories of the scale factor. I'm not aware of any model with a sine-like scale factor, but there are people considering cyclical cosmologies. But they would still be a series of big bangs and big crunches.
That is not what I'm asking. I'm asking if expansion and contraction could fluctuate in perpetuity, like stress waves through a block of jello.