In this paper we study the corrections to the Friedmann equations due to fast fluctuations of the universe scale factor. Such fast quantum fluctuations were recently proposed as a potential solution of the cosmological constant problem. They also induce strong changes to the current sign and magnitude of the average cosmological force, thus making it one of the potential probable causes for the modification of Newtonian dynamics in galaxy-scale systems. It appears that quantum fluctuations of the scale factor also modify the Friedmann equations, leading to considerable modification of cosmological evolution. In particular, they give rise to late-time accelerated expansion of the universe, and they may also considerably modify the effective universe potential.
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