String axiverse

String theory suggests the simultaneous presence of many ultralight axions, possibly populating each decade of mass down to the Hubble scale 10^-33 eV. Conversely the presence of such a plenitude of axions (an axiverse) would be evidence for string theory, since it arises due to the topological complexity of the extra-dimensional manifold and is ad hoc in a theory with just the four familiar dimensions. We investigate how several upcoming astrophysical experiments will be observationally exploring the possible existence of such axions over a vast mass range from 10^-33 eV to 10^-10 eV. Axions with masses between 10^-33 eV to 10^-28 eV can cause a rotation of the cosmic microwave background polarization that is constant throughout the sky. The predicted rotation angle is independent of the scale of inflation and the axion decay constant, and is of order 1/137 --within reach of the just launched Planck satellite. Axions in the mass range 10^-28 eV to 10^-18 eV give rise to multiple steps in the matter power spectrum, providing us with a snapshot of the axiverse that will be probed by galaxy surveys--such as BOSS, and 21 cm line tomography. Axions in the mass range 10^-22 eV to 10^-10 eV can affect the dynamics and gravitational wave emission of rapidly rotating astrophysical black holes through the Penrose superradiance process. When the axion Compton wavelength is of order of the black hole size, the axions develop superradiant atomic bound states around the black hole nucleus. Their occupation number grows exponentially by extracting rotational energy and angular momentum from the ergosphere, culminating in a rotating Bose-Einstein axion condensate emitting gravitational waves. For black holes lighter than 10^7 solar masses accretion cannot replenish the spin of the black hole, creating mass gaps in the spectrum of rapidly rotating black holes that diagnose the presence of destabilizing axions. In particular, the highly rotating black hole in the X-ray binary LMC X-1 implies an upper limit on the decay constant of the QCD axion f₀210^17 GeV, much below the Planck mass. This reach can be improved down to the grand unification scale f₀210^16 GeV, by observing smaller stellar mass black holes.