String Axiverse

TL;DR

The paper proposes the string axiverse: a plenitude of ultralight axions predicted by string theory, with masses spanning many orders of magnitude and observable consequences across cosmology and black hole physics. It develops three complementary observational channels—CMB polarization rotation, small-scale structure suppression, and black hole superradiance—that together could reveal multiple axion species and their fundamental parameters, largely independent of the inflationary scale or initial misalignment. By connecting axion phenomenology to the cosmological constant landscape and to realistic astrophysical environments, the work argues that a detection of multiple axions would provide strong evidence for string theory and offer a unique window into high-energy theory and early-universe dynamics. The analysis also discusses robustness in realistic settings, potential gravitational-wave signals, and future directions including decays and warped scenarios.

Abstract

String theory suggests the simultaneous presence of many ultralight axions possibly populating each decade of mass down to the Hubble scale 10^-33eV. 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 upcoming astrophysical experiments will explore the existence of such axions over a vast mass range from 10^-33eV to 10^-10eV. Axions with masses between 10^-33eV to 10^-28eV cause a rotation of the CMB polarization that is constant throughout the sky. The predicted rotation angle is of order α~1/137. Axions in the mass range 10^-28eV to 10^-18eV give rise to multiple steps in the matter power spectrum, that will be probed by upcoming galaxy surveys. Axions in the mass range 10^-22eV to 10^-10eV 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 from the ergosphere, culminating in a rotating Bose-Einstein axion condensate emitting gravitational waves. This mechanism creates mass gaps in the spectrum of rapidly rotating black holes that diagnose the presence of axions. The rapidly rotating black hole in the X-ray binary LMC X-1 implies an upper limit on the decay constant of the QCD axion f_a<2*10^17GeV, much below the Planck mass. This reach can be improved down to the grand unification scale f_a<2*10^16GeV, by observing smaller stellar mass black holes.

Figures (9)

• Figure 1: Map of the Axiverse: The signatures of axions as a function of their mass, assuming $f_a \approx M_{GUT}$ and $H_{inf}\sim 10^8$ eV. We also show the regions for which the axion initial angles are anthropically constrained not to over-close the Universe, and axions diluted away by inflation. For the same value of $f_a$ we give the QCD axion mass. The beginning of the anthropic mass region ($2 \times 10^{-20}$ eV) as well as that of the region probed by density perturbations ($4 \times 10^{-28}$ eV) are blurred as they depend on the details of the axion cosmological evolution (see Section \ref{['steps']}). $3 \times 10^{-18}$ eV is the ultimate reach of density perturbation measurements with 21 cm line observations. The lower reach from black hole super-radiance is also blurred as it depends on the details of the axion instability evolution (see Section \ref{['BHreach']}). The region marked as "Decays", outlines very roughly the mass range within which we expect bounds or signatures from axions decaying to photons, if they couple to $\vec{E} \cdot \vec{B}$. We will discuss axion decays in detail in a companion paper.
• Figure 2: Evolution of different physical momentum scales as a function of the scale factor. The horizontal long-dashed line corresponds to the axion mass. The short-dashed line shows Hubble. The dash-dotted line shows the evolution of the Jeans scale. Finally, three solid lines correspond to physical momenta of long and short modes and of the mode with $k=k_m$.
• Figure 3: Suppression of the power spectrum observed today as a function of the comoving monentum. $\delta_k$ has been normalized to the value at large scales and we have assumed ${\Omega_a \over \Omega_m}=0.01$.
• Figure 4: A time evolution of the axion field for different initial conditions (left panel) and an enhancement factor $P(\theta)$ for the axion abundance as a function of a probability for different initial axion values (right panel).
• Figure 5: The effective potential of Eq. (\ref{['schrodpot']}). Depicted are the ergoregion, to the left, with the horizon at $r^* \rightarrow - \infty$, the centrifugal barrier (whose height depends on the angular momentum of a mode), the potential well to the right of it, and the asymptotic mass barrier which plays the role of the mirror that reflects the escaping Penrose fragment back. The relevant modes will be the states bound in the potential, and leaking through the barrier towards the horizon.