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 ( IILM ) , 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 } \leq 2.8 ( \pm 2 ) \times 10 ^ { 11 } \mathrm { GeV } or m _ { a } \geq 21 ( \pm 2 ) \mathrm { \mu 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However , this is superseded by axion string radiation which leads to f _ { a } \lesssim 3.2 ^ { +4 } _ { -2 } \times 10 ^ { 10 } \mathrm { GeV } or m _ { a } \gtrsim 0.20 ^ { +0.2 } _ { -0.1 } \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 \theta _ { a } \to \pi .
In particular , we find that inflationary dark matter axions can have masses as high as 0.01–1 \mathrm { meV } , covering the whole thermal axion range , with values of H _ { I } up to 10 ^ { 9 } GeV .
Quantum fluctuations during inflation exclude dominant dark matter axions with masses above m _ { a } \lesssim 1 meV .