Abstract
The weak gravity conjecture imposes severe constraints on natural inflation. A trans-Planckian axion decay constant can only be realized if the potential exhibits an additional (subdominant) modulation with sub-Planckian periodicity. The resulting wiggles in the axion potential generate a characteristic modulation in the scalar power spectrum of inflation which is logarithmic in the angular scale. The compatibility of this modulation is tested against the most recent Cosmic Microwave Background (CMB) data by Planck and BICEP/Keck. Intriguingly, we find that the modulation completely resolves the tension of natural inflation with the CMB. A Bayesian model comparison reveals that natural inflation with modulations describes all existing data equally well as the cosmological standard model $\Lambda$CDM. In addition, the bound of a tensor-to-scalar ratio r > 0.002 correlated with a striking small-scale suppression of the scalar power spectrum occurs. Future CMB experiments could directly probe the modulation through their improved sensitivity to smaller angular scales and possibly the measurement of spectral distortions. They could, thus, verify a key prediction of the weak gravity conjecture and provide dramatic new insights into the theory of quantum gravity.
Highlights
The cosmic microwave background (CMB) provides a window to physics at very high energy scales
In order to solve the EinsteinBoltzmann equations for cosmological perturbations and compute the theoretical predictions, such as the CMB temperature and polarization power spectra, we modified the current version of the Code for Anisotropies in the Microwave Background (CAMB) [24], so that the primordial spectra9 are given as (28) and (29)
Turning first to natural inflation with the pure cosine potential, we confirm a mild tension with CMB data
Summary
The cosmic microwave background (CMB) provides a window to physics at very high energy scales It probes the era of cosmic inflation and could even contain imprints from the theory of quantum gravity. Even more important is the application of the WGC to nonperturbative axion physics [1,2,3,4,5,6] This is because axions are the prime candidates to realize largefield inflation within a consistent theory of quantum gravity—for which string theory is the leading candidate. The axion potential exhibits the desired cosine shape with additional wiggles which result from the higher harmonics in the modular functions It is, not surprising that modular functions play a crucial role since—as the WGC itself—they are deeply connected to the duality symmetries of string theory. We will make exciting predictions for spectral distortions in the CMB which can be tested with future satellite missions
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