Ripples on a pond spread in circles from a thrown stone. Now imagine the pond itself begins to tremble — the water oscillates not only from the stone but also on its own. That's roughly how gravitational waves behave in space where a special scalar field pulsates.
The authors built a mathematical model of such trembling. They applied a method that lets you peer into the 'microscopic' structure of both the field and the waves simultaneously. It turned out that the field's instability adds new features to the waves — terms appear that are absent in the usual situation. These additions tend toward infinity, and physicists have to 'tame' them with counterterms — special corrections that remove the nonsense.
The most interesting part is the discrepancy between two ways of accounting for the background. When the field is treated as static, versus when it's part of a dynamical system, the results don't match. The authors suspect this is because the background in their model is artificially fixed. In a real curved Universe, such a mismatch shouldn't occur.
Scalar fields like the one considered in the paper are sometimes invoked to explain dark energy, the mysterious cause of the Universe's accelerated expansion.
In Carl Sagan's novel 'Contact', an alien signal contained instructions for building a machine that works on vibrations of spacetime itself.