Relaxing the Cosmological Moduli Problem by Low-scale Inflation

Abstract: We show that the cosmological abundance of string axions is much smaller than naive estimates if the Hubble scale of inflation, $H_{\rm inf}$, is sufficiently low (but can still be much higher than the axion masses) and if the inflation lasts sufficiently long. The reason is that the initial misalignment angles of the string axions follow the Bunch-Davies distribution peaked at the potential minima. As a result, the cosmological moduli problem induced by the string axions can be significantly relaxed by low-scale inflation, and astrophysical and cosmological bounds are satisfied over a wide range of the mass without any fine-tuning of the initial misalignment angles. Specifically, the axion with its decay constant $f_\phi = 10^{16}$\,GeV satisfies the bounds over $10^{-18}{\rm \, eV} \lesssim m_\phi \lesssim 10{\rm\,TeV}$ for $H_{\rm inf} \lesssim 10{\rm\,keV}- 10^{6}$\,{\rm GeV}. We also discuss cases with multiple axions and the QCD axion.