Your concept is accepted (with a few changes of terms) by some cosmologists. The big exception would be the concept of 'space'. Matter and energy don't expand 'into' space (your cube) but create space and time. The word 'infinity' means all types of things but many see a 'finite' universe and 'infinite time' as a contradiction. A universe that stops expanding ceases to create it's own time and space and therefore is not 'infinite'.

One argument against an 'exact' replay of expansion and contraction is that the universe does not appear uniform. All particles are not equal distant from eachother so how could uneveness of energy and matter exist in a universe that repeats itself.