Gravitational waves: Exploring the strongly curved side of the Universe

Gravitational waves from the mergers of five binary black holes and one binary neutron star were detected in the past two years by the advanced LIGO and Virgo detectors. These detections allowed our Universe to be observed in gravitational waves for the first time, and they have tested the predictions of general relativity for dynamical and strongly gravitating systems. I will discuss these results and also highlight a few additional examples of ways in which gravitational waves can shed light on open questions in theoretical physics and astrophysics. One involves the gravitational-wave memory effect, which is a constant change in the gravitational-wave strain produced by the energy that gravitational waves and matter carry away from an isolated system. I will describe the challenges in detecting the memory with LIGO and Virgo, and how the memory is related to the symmetries and conserved quantities of isolated gravitating systems. A second involves using precision astrometry to detect a stochastic background of gravitational waves from astrophysical, and potentially even cosmological, sources. With the upcoming data release from the Gaia mission, it will likely be possible to place improved constraints on the stochastic background at frequencies higher than those coming from the cosmic microwave background, but below those of pulsar timing searches. I will show how these constraints can be determined. Finally, I will discuss gravitational waves from a compact object orbiting an intermediate mass black hole surrounded by a dark matter spike. I will describe how details about the dark matter distribution can be imprinted in the emitted gravitational waves.