The backdrop against which cosmology is set is provided by the geometry of spacetime. As often pointed out in this forum, General Relativity has revealed that this geometry is not fixed and eternal, but changes as the structure of the universe evolves from an ultradense, ultrahot but formless plasma into the objects we now observe in our night skies. And much else. The second law of thermodynamics prescibes that during this evolution entropy must increase. Penrose, in his Road to Reality, Chap. 27 explains how an increase of entropy can occur (despite the random initial state of the universe) as gravitational degrees of freedom are taken up during structure formation. He presents and illustrates his arguments in terms of the coarse-graining of phase space, analagous to the coarse graining of the phase space of a perfect gas. Phase space is an abstract and convenient tool for simplifying the the evolution of a multi-component system (such as a gas) by representing its evolution as a single ergodically wandering curve in phase space. But phase space is derived from the coordinate spaces we use to quantify 'real space' (whatever that may be!) and, as with spatial sections of spacetime , these coordinate spaces must change and evolve, expand and locally distort, as the universe itself changes locally or globally, and evolves. When Chance, Nature or Something invents, deploys or activates (words are difficult here) autocatalytic tricks (I'm thinking of gravity or the much later inception of DNA) will this, together with the evolution of spacetime, not profoundly alter the coase-graning of phase space and with it, how entropy increases as the universe explores its future?