Random thought of the day: inflating universe = accelerating time?

Disclaimer: Just as I am not a historian, but rather as Dan Carlin says a fan of history, I am also not a physicist, but merely a fan of physics.
Do you ever get a brain worm that you just can’t shake?  No, I don’t mean a physical parasite, but something you just can’t get out of your head no matter what you try?  For most people it’s a song.  For me it’s been this the last few days: is the expanding universe causing them to accelerate?
A little background.  I picked a copy of Max Tegmark’s Our Mathematical Universe a few weeks ago and am about 100 pages in.
<complete tangent> I swear to all of you that read this that I will finish at least half of the books I am in the middle of before I start anything else.  I just finished one that interrupted OMU (review coming soon) so will go back to OMU, then loop my way back to Influence.  Then back the finish the Problem of Political Authority.  Then, perhaps I can actually look at my too read pile without an overwhelming sense of defeat.</complete tangent>
I feel like I am in some sort of book based Inception).  I think I’ve groked most of it, but one can never be quite sure when reading something like this.  One theory he talks about early on that I’ve heard elsewhere is the idea that the universe is expanding.  The typical explanation involves dots on a ballon that is being blown up.  The dots themselves get bigger and further apart.
The inflation part is not what’s stuck in my head.  Rather it’s a seemingly random (and completely unsupported by data or even the flimsiest of theories, but just a intuitive sense that one would cause the other.  Einstein proved that space and time are related, so wouldn’t the expansion of space have some effect on time?  Being a fan of physics, it may well be that this relationship is well understood by real physicists, but I had a Eureka feeling when it first occurred to me.  And no, not because it explains why we’re all getting fatter and there is less time in each day.  Rather there is just something satisfying about developing a new concept, even if it proves out to be wrong or only just new to you.  Discovery is exciting no matter what.