The cosmos is far from being mostly empty space.
Space is more aptly defined by what is not in it, rather than the wide assortment of things that are. A gas disperses evenly within a closed area until it uniformly fills the openness that confines it. In similar fashion, matter seems manifestly intent to occupy the full extent of whatever spatial enclosure would prevent its boundless expansion. The new theories about the existence of Dark matter and Dark energy demonstrate how little we actually know and how much more there is to learn.
The logical mind imagines the never-ending straight line. And in so doing, confronts the incomprehensible aspects of infinity. Or the equally incomprehensible idea that multi-dimensional space/time is ultimately curved back on itself. But as a question, might not linear projections, both theoretical and real, unhampered by gravity and other forces, travel tangential paths that take them forever farther from their points of origin?
Regions of truly empty space are still occupied by an immaterial presence of potentially viable physical forces such as time, gravity, inertia, heat, and especially cold temperatures. How cold is absolute space? How is the temperature of matter, in space, affected by its motion through it? And, of course, as previously mentioned, those two new darlings of astrophysics: Dark energy and Dark matter.
The existence of matter in any location exerts an influence on all other regions. Unlike our more traditional notions of magnetism, gravity is instead a distortion of the area that surrounds something with mass. With respect to evolution, both organic and geologic in nature, slow changes over long periods of time are part of a process called Uniformitarianism. The occurrence of sudden changes, over brief intervals, is termed Catastrophism. Evolutionary jumps are the result of interruptions of Uniformitarianism by Catastrophism. The otherwise coherent whole that changes due to fluctuations or deviations from Uniformitarianism.
Results occur that are unexpected and interesting during such interferences. The accompanying process is called Punctuated Equilibrium, which is the idea of evolutionary strides based on random, catastrophic (cataclysmic) events. I discuss this more in the essay entitled Punctuated Equilibrium.
Which doesn't refer, by the way, to the proper grammatical use of the word, equilibrium.