Irreducible Axion Background

Searches for dark matter decaying into photons constrain its lifetime to be many orders of magnitude larger than the age of the Universe. A corollary statement is that the abundance of any particle that can decay into photons over cosmological timescales is constrained to be much smaller than the cold dark-matter density. We show that an irreducible freeze-in contribution to the relic density of axions is in violation of that statement in a large portion of the parameter space. This allows us to set stringent constraints on axions in the mass range 100 eV–100 MeV. At 10 keV our constraint on a photophilic axion is <math display="inline"><mrow><msub><mrow><mi>g</mi></mrow><mrow><mi>a</mi><mi>γ</mi><mi>γ</mi></mrow></msub><mo>≲</mo><mn>8.1</mn><mo>×</mo><msup><mrow><mn>10</mn></mrow><mrow><mo>-</mo><mn>14</mn></mrow></msup><mtext> </mtext><mtext> </mtext><msup><mrow><mi>GeV</mi></mrow><mrow><mo>-</mo><mn>1</mn></mrow></msup></mrow></math>, almost 3 orders of magnitude stronger than the bounds established using horizontal branch stars; at 100 keV our constraint on a photophobic axion coupled to electrons is <math display="inline"><mrow><msub><mrow><mi>g</mi></mrow><mrow><mi>a</mi><mi>e</mi><mi>e</mi></mrow></msub><mo>≲</mo><mn>8.0</mn><mo>×</mo><msup><mrow><mn>10</mn></mrow><mrow><mo>-</mo><mn>15</mn></mrow></msup></mrow></math>, almost 4 orders of magnitude stronger than the present results. Although we focus on axions, our argument is more general and can be extended to, for instance, sterile neutrinos.