# Relaxing the Cosmological Moduli Problem by Low-scale Inflation

## TL;DR

This paper demonstrates that low-scale inflation can significantly reduce the cosmological abundance of string axions, alleviating the moduli problem without fine-tuning, over a broad range of axion masses and decay constants.

## Contribution

It introduces a mechanism where low-scale inflation naturally suppresses axion abundance by aligning initial misalignment angles, relaxing cosmological constraints without fine-tuning.

## Key findings

- Axion abundance is reduced with low Hubble scale inflation.
- Bounds on axion mass and decay constant are satisfied over wide parameter ranges.
- The mechanism applies to multiple axions and the QCD axion.

## 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.