Gravitational Axiverse Spectroscopy: Seeing the Forest for the Axions

We consider inflationary models with multiple spectator axions coupled to dark gauge sectors via Chern-Simons (CS) terms. The energy injection into Abelian gauge fields from the axions engenders a multi-peak profile for scalar and tensor spectra. We highlight the constraining power of CMB spectral distortions on the scalar signal and discuss the conditions under which spectator sectors can account for the recently observed stochastic gravitational wave (GW) background in the nHz range. Given the tantalizing prospect of a multi-peak ``GW forest'' spanning several decades in frequency, we elaborate on possible ultraviolet origins of the spectator models from Type IIB orientifolds. String compactifications generically produce a multitude of axions, the ``Axiverse'', from dimensional reduction of p-form gauge fields. The CS coupling of such axions to dark gauge fields in the worldvolume theory of D7-branes can be tuned via multiple brane wrappings and/or quantized gauge field strengths. If string axions coupled to Abelian gauge fields undergo slow-roll during inflation, they produce GW signals with peaked frequency distribution whose magnitude depends on the details of the compactification. We discuss the restrictions on spectator models from consistency and control requirements of the string compactification and thereby motivate models that may live in the string landscape as opposed to the swampland.