Emergent gravity can be applied to a large $N$ matrix model by considering
the vacuum of a noncommutative (NC) Coulomb branch that satisfies the
Heisenberg algebra. Due to the fact that IR fluctuations in the NC Coulomb
branch always pair with UV fluctuations, this UV/IR mixing is extendable to a
macroscopic scale. These vacuum fluctuations in the NC Coulomb branch are
described by a four-dimensional NC $U(1)$ gauge theory. The order parameter for
the vacuum fluctuations is given by random four-vectors that have their own
causal structure in the commutative limit unlike the conventional cosmological
models based on a scalar field theory coupled to gravity. We show that their
causal structure results in the different nature of gravitational interactions
so that space-like fluctuations give rise to the repulsive gravitational force
while time-like fluctuations generate the attractive gravitational force. Given
the fact that the fluctuations are random in nature and we live in a
(3+1)-dimensional spacetime, the ratio of the repulsive vs. attractive
components ends up being 3:1 = 75:25, which is interestingly consistent with
the dark components of the current universe. If we include ordinary matters
acting as an attractive gravitational force, the emergent gravity could more
accurately explain the dark side of our universe. This work is an expanded
version of the conference proceedings (Yang in EPJ Web Conf 168:03006, 2018).
