It has been known for about hundred years that the universe is expanding, but an impressive discovery came at the end of 20th century, when it was found that the universe is expanding with acceleration. Since then, many models have been developed in cosmology to explain this phenomenon. One of the possible elucidations is that the theory of gravity must be modified at the classical level. However, many such models have already been excluded by gravitational wave experiments. Therefore, one must put a more critical question: could accelerated expansion of the universe be a phenomenon of quantum gravity? Here, we review the basic models of how one explains the origin of dark energy or the cosmological constant in metastring theory, discrete approaches to quantum gravity, group field theory, non-commutative geometry, causal dynamical triangulation, asymptotic safety, and models based on holography and entropic gravity. At the end of a newly formed approach to the quantization of gravity, we mention the ring paradigm, which may, after application to cosmology, naturally model the late-time accelerated expansion epoch in the universe. What is most remarkable, though, is that the final formulation of this theory may ultimately solve the old problem of the cosmological constant.
Novák et al. (Wed,) studied this question.