Like a cyclical interaction with a neighbor brane which is essentially another universe? Because that's the ekpyrotic universe model. And it fits with your imagination.
The first hit from DuckDuckGo for 'ekpyrotic' is the Wikipedia page https://en.wikipedia.org/wiki/Ekpyrotic_universe . It describes the reason Steinhardt created that word as the name for the model.
> We propose a cosmological model in which the universe undergoes an endless sequence of cosmic epochs each beginning with a ‘bang’ and ending in a ‘crunch.’ The temperature and density are finite at each transition from crunch to bang. Instead of having an inflationary epoch, each cycle includes a period of slow accelerated expansion (as recently observed) followed by slow contraction. The combination produces the homogeneity, flatness, density fluctuations and energy needed to begin the next cycle.
