Gravitational waves can be used to study the expansion of the universe by measuring the rate of change in the distance between two or more objects in space. This is because as the universe expands, the objects in it move further apart, and the gravitational waves emitted by these objects will exhibit a characteristic 'signature' that is related to the rate of expansion.

To measure the expansion of the universe using gravitational waves, astronomers use a detector such as the Laser Interferometer Gravitational-Wave Observatory (LIGO), which consists of two widely separated interferometers that measure the time taken for light to travel between mirrors in the interferometer arms. When a gravitational wave passes by, it causes the distance between the mirrors to change, and this can be detected as a change in the time it takes for the light to travel between the mirrors.

The rate of expansion of the universe can be inferred from the observed gravitational waves by comparing the observed 'stretch' of the gravitational wave signal with the predicted 'stretch' that would be caused by the expansion of the universe. By making precise measurements of the stretching of the gravitational wave signal, astronomers can obtain an accurate measurement of the rate of expansion of the universe.

In addition to measuring the rate of expansion, gravitational waves can also be used to study other aspects of the universe, such as the presence of massive black holes and neutron stars, and the properties of dark matter and dark energy. By studying gravitational waves, astronomers can gain a deeper understanding of the universe and its history, and may even be able to uncover new and unexpected phenomena.