Axion cosmology revisited

The misalignment mechanism for axion production depends on the temperature-dependent axion mass. The latter has recently been determined within the interacting instanton liquid model, and provides for the first time a well-motivated axion mass for all temperatures. We reexamine the constraints placed on the axion parameter space in the light of this new mass function. Taking this mass at face value, we find an accurate and updated constraint ${f}_{a}\ensuremath{\le}2.8(\ifmmode\pm\else\textpm\fi{}2)\ifmmode\times\else\texttimes\fi{}{10}^{11}\text{ }\text{ }\mathrm{GeV}$ or ${m}_{a}\ensuremath{\ge}21(\ifmmode\pm\else\textpm\fi{}2)\text{ }\text{ }\ensuremath{\mu}\mathrm{eV}$ from the misalignment mechanism in the classic axion window (thermal scenario). However, this is superseded by axion string radiation which leads to ${f}_{a}\ensuremath{\lesssim}{3.2}_{\ensuremath{-}2}^{+4}\ifmmode\times\else\texttimes\fi{}{10}^{10}\text{ }\text{ }\mathrm{GeV}$ or ${m}_{a}\ensuremath{\gtrsim}{0.20}_{\ensuremath{-}0.1}^{+0.2}\text{ }\text{ }\mathrm{meV}$. In this analysis, we take care to precisely compute the effective degrees of freedom and, to fill a gap in the literature, we present accurate fitting formulas. We solve the evolution equations exactly, and find that analytic results used to date generally underestimate the full numerical solution by a factor 2--3. In the inflationary scenario, axions induce isocurvature fluctuations and constrain the allowed inflationary scale ${H}_{I}$. Taking anharmonic effects into account, we show that these bounds are actually weaker than previously computed. Considering the fine-tuning issue of the misalignment angle in the whole of the anthropic window, we derive new bounds which open up the inflationary window near ${\ensuremath{\theta}}_{a}\ensuremath{\rightarrow}\ensuremath{\pi}$. In particular, we find that inflationary dark matter axions can have masses as high as $0.01--1\text{ }\text{ }\mathrm{meV}$, covering the whole thermal axion range, with values of ${H}_{I}$ up to ${10}^{9}\text{ }\text{ }\mathrm{GeV}$. Quantum fluctuations during inflation exclude dominant dark matter axions with masses above ${m}_{a}\ensuremath{\lesssim}1\text{ }\text{ }\mathrm{meV}$.