It is common belief that gravity is an attractive interaction between all
things with mass or energy, affecting the motion of objects at the macroscopic
scale and determining the large-scale structure of the universe. Contrary to
the conventional cognition, here we reveal that gravitational repulsion is also
ubiquitous in quantum systems -- the anomalous response of the position of the
particles at (topologically) excited states to the gravitational field in
confined systems. We prove that this anti-gravitational phenomenon results from
a principle called `quantum-state exclusion' inherited from the orthogonality
of quantum states. We further predict that, in an inflating space, this
gravitational anomaly may cause quantum matter in excited states to expand even
faster than space, leading to an observable accumulation of quantum matter near
the boundary of the space. These unique phenomena can be simulated in ultracold
atom experiments by using Bose-Einstein condensates with solitons. The
accelerating expansion phenomenon in quantum systems also sheds new light on
understanding the evolution of the universe, where the vacuum state may also be
an excitation with topological defects.Comment: 7 pages, 2+2 figures (abstract and introduction are updated