My view these days, is that neither space nor time exist in the same way as ponderable matter. They are simply dimensions or numerical locations which were created during the big bang. Also, that the expansion of space is being driven by matter being lost everywhere throughout the Universe. Matter bends space into gravity wells. As mass is lost to energy, all the gravity wells, both large and small, relax, and space then expands.
Matter is being converted into energy in so many different ways everywhere throughout the universe. We could therefore expect the rate of expansion of space to vary from the first moments of the big bang during matter anti-matter annihilation, which is called inflation, until today which is called dark energy expansion. This is what we observe, the Hubble constant changes over billions of years.
There may also be contributions to the expansion of space from other sources also. For example, radiation pressure, or pull from the rest of the expanding type 1 multiverse. I usually tend to believe that everything which happens inside our universe is as a result of what is happening inside our universe, and not from some magical force beyond it. However, an important counter view to this may be that the big bang may be continuing today, and the Universe is still being inflated from the dark dimensions beyond. By the dark dimensions I refer to the dimensions which are being continually fed right now from black hole singularities in our own universe. There could be some similarities in such a cycle to the water cycle here on earth.
In fact, perhaps all of the above is true and all of it is happening all of the time? Perhaps the Universe goes into reverse during periods of drought?