Question

Do quantum fluctuations cause variations in energy density across space?

Answer 1

No.

"Quantum fluctuations" are not actual fluctuations - at least not if you choose to add any by suitable interpretation of quantum theory and even then, any such interpretation must be consistent with observation and observation is not consistent with the things that actually affect it undergoing real fluctuation.

hope this helps you

Answer 2

No...........quantum fluctuations do not cause variations energy density across space...