Scalar dark energy models and scalar–tensor gravity:theoretical explanations for the accelerated expansion of the present Universe

The reason for the present accelerated expansion of the Universe stands as one of the most profound questions in the realm of science, with deep connections to both cosmology and fundamental physics. From a cosmological point of view, physical models aimed at elucidating the observed expansion can be categorized into two major classes: dark energy and modified gravity. We review various major approaches that employ a single scalar field to account for the accelerating phase of our present Universe. Dynamic system analysis was employed in several important models to find cosmological solutions that exhibit an accelerating phase as an attractor.For scalar field models of dark energy, we consistently focused on addressing challenges related to the fine-tuning and coincidence problems in cosmology, as well as exploring potential solutions to them. For scalar–tensor theories and their generalizations, we emphasize the importance of constraints on theoretical parameters to ensure overall consistency with experimental tests. Models or theories that could potentially explain the Hubble tension are also emphasized throughout this review.