Time can have 2 different connotations. One is inherent to an entity in spacetime by itself, say a lonely radioactive atom. It may decay or it may not decay, independently of what's going on around it. But another involves interactions between particles, for example "it takes 60 seconds for microwave radiation of x frequency and amplitude to warm up water from 20C to 50C". If we follow the assumed accelerated expansion of the universe, atoms and other structures will become farther away from each other, towards a heath death. There will be a time when particles will get so far away from each other, and space in between them will be expanding so fast, that interaction between them will no longer be possible. In between now and then, all events which involve interaction between particles will gradually take more time, because the distance between them will be increasing. Perhaps the microwave source will need not 60 seconds but one month to warm up that water from 20C to 30C, because the space between the radiation source and the target is expanding. Any chemical reaction which is now believed to happen at a certain rate will take much longer, and so on. An hypothetical civilization living in that far future in an expanded space, will see the chemical reaction taking a longer time to happen than we do now. If we understand Time as the rate at which events happen, could we say that the space expansion slows the rate of time?