Improved hot dark matter bound on the QCD axion

We obtain a reliable cosmological bound on the axion mass <math display="inline"><msub><mi>m</mi><mi>a</mi></msub></math> by (1) deriving the production rate directly from pion-pion scattering data, which overcomes the breakdown of chiral perturbation theory and results in <math display="inline"><mo>∼</mo><mn>30</mn><mo>%</mo></math> differences from previous estimates; (2) including momentum dependence in the Boltzmann equations for axion-pion scatterings, which enhances the relic abundance by <math display="inline"><mo>∼</mo><mn>40</mn><mo>%</mo></math>. Using present cosmological datasets we obtain <math display="inline"><msub><mi>m</mi><mi>a</mi></msub><mo>≤</mo><mn>0.24</mn><mtext> </mtext><mtext> </mtext><mi>eV</mi></math>, at 95% C.L. We also constrain the sum of neutrino masses, <math display="inline"><mrow><mo>∑</mo><msub><mrow><mi>m</mi></mrow><mrow><mi>ν</mi></mrow></msub><mo>≤</mo><mn>0.14</mn><mtext> </mtext><mtext> </mtext><mi>eV</mi></mrow></math> at 95% C.L., in the presence of relic axions and neutrinos. Finally, we show that reliable nonperturbative calculations above the QCD crossover are needed to exploit the reach of upcoming cosmological surveys for axion detection.