Friedmann equation with quantum potential

Abstract

Abstract. Friedmann equations are used to describe the evolution of the universe. Solving Friedmann equations for the scale factor indicates that the universe starts from an initial singularity where all the physical laws break down. However, the Friedmann equations are well describing the late-time or large scale universe. Hence now, many physicists try to find an alternative theory to avoid this initial singularity. In this paper, we generate a version of first Friedmann equation which is added with an additional term. This additional term contains the quantum potential energy which is believed to play an important role at small scale. However, it will gradually become negligible when the universe evolves to large scale.

Effect of Fast Scale Factor Fluctuations on Cosmological Evolution

“…Another interesting consequence of Eqs. (17,18) is that the presence of fast cosmological scale factor oscillations generically reproduces the late-time accelerated expansion of the universe regardless of its matter and energy content. This is quite obvious from Eq.…”

“…We should also note that the effective universe potential in the quantum Friedmann models exhibits a similar unstable point (see for example ref. [17]). Therefore, it is reasonable to expect that random and incoherent quantum fluctuations of the scale factor should lead to Kapitza effect, especially since there is no reason to expect that the quantum state of the universe within the scope of the quantum Friedmann model will be a scale factor eigenstate.…”