Gravitational probes of ultra-light axions
  The axion is a hypothetical, well-motivated dark-matter particle whose
existence would explain the lack of charge-parity violation in the strong
interaction. In addition to this original motivation, an `axiverse' of
ultra-light axions (ULAs) with masses $10^{-33}\,{\rm eV}\lesssim m_{\rm
a}\lesssim 10^{-10}\,{\rm eV}$ also emerges from string theory. Depending on
the mass, such a ULA contributes to the dark-matter density, or alternatively,
behaves like dark energy. At these masses, ULAs' classical wave-like properties
are astronomically manifested, potentially mitigating observational tensions
within the $\Lambda$CDM paradigm on local-group scales. ULAs also provide
signatures on small scales such as suppression of structure, interference
patterns and solitons to distinguish them from heavier dark matter candidates.
Through their gravitational imprint, ULAs in the presently allowed parameter
space furnish a host of observational tests to target in the next decade,
altering standard predictions for microwave background anisotropies, galaxy
clustering, Lyman-$\alpha$ absorption by neutral hydrogen along quasar
sightlines, pulsar timing, and the black-hole mass spectrum.
