The journey beyond Einstein：modified gravity theories and cosmological models

In cosmological research, although the general theory of relativity has achieved success on local scales, it faces difficulties in explaining cosmic-scale phenomena such as abnormal galactic rotation curves and the accelerated expansion of the universe. Moreover, the nature of dark matter and dark energy remains unclear. These issues have prompted scientists to explore modified gravitational theories and cosmological models, which offer new perspectives on cosmological puzzles by adjusting the basic assumptions of gravity. For example, f(R) gravity can drive the inflation of the early universe and simulate the effects of dark energy in the late stage; scalar-tensor theories introduce dynamic scalar fields to regulate the strength of gravity; and braneworld models explain the accelerated expansion of the universe using the gravitational leakage of extra dimensions. Gravitational waves, as probes of spacetime, open up a new window for testing gravitational theories and studying the evolution of the universe. For instance, the joint observation of GW170817 constrained the deviation of the propagation speed of gravitational waves from the speed of light. In the future, astronomical projects such as the Euclid satellite and space-based gravitational wave detectors will provide more data to further test the modified theories, promoting our understanding of the nature of the universe and helping physics move towards a new age.