Ultrarelativistic freeze-out during reheating

We perform a thorough investigation of (ultra)relativistic freeze-out (UFO) during reheating. While the standard WIMP (nonrelativistic freeze-out) and FIMP (freeze-in) paradigms have been explored in detail during the reheating epoch, UFO has not been systematically studied, despite the fact that it is operative in a broad region of parameter space. Although dark matter (DM) is “hot” at the time of relativistic freeze-out, we show that it can easily undergo enough cooling by the time of structure formation to be compatible with <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mi mathvariant="normal">Λ</a:mi> <a:mi>CDM</a:mi> </a:math> . Unlike standard WIMP-like freeze-out, there can be significant out-of-equilibrium DM production after UFO, similar to the freeze-in mechanism. However, unlike freeze-in, UFO can accommodate much stronger couplings. The UFO parameter space consistent with <d:math xmlns:d="http://www.w3.org/1998/Math/MathML" display="inline"> <d:msub> <d:mi mathvariant="normal">Ω</d:mi> <d:mi>χ</d:mi> </d:msub> <d:msup> <d:mi>h</d:mi> <d:mn>2</d:mn> </d:msup> <d:mo>=</d:mo> <d:mn>0.12</d:mn> </d:math> is quite large, with DM masses spanning about 13 orders of magnitude ( <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"> <g:msup> <g:mn>10</g:mn> <g:mrow> <g:mo>−</g:mo> <g:mn>7</g:mn> </g:mrow> </g:msup> <g:mtext> </g:mtext> <g:mtext> </g:mtext> <g:mi>GeV</g:mi> <g:mo>≲</g:mo> <g:msub> <g:mi>m</g:mi> <g:mi>χ</g:mi> </g:msub> <g:mo>≲</g:mo> <g:msup> <g:mn>10</g:mn> <g:mn>6</g:mn> </g:msup> <g:mtext> </g:mtext> <g:mtext> </g:mtext> <g:mi>GeV</g:mi> </g:math> ), reheating temperatures spanning 17 orders of magnitude ( <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"> <i:msup> <i:mn>10</i:mn> <i:mrow> <i:mo>−</i:mo> <i:mn>2</i:mn> </i:mrow> </i:msup> <i:mtext> </i:mtext> <i:mtext> </i:mtext> <i:mi>GeV</i:mi> <i:mo>≲</i:mo> <i:msub> <i:mi>T</i:mi> <i:mrow> <i:mi>RH</i:mi> </i:mrow> </i:msub> <i:mo>≲</i:mo> <i:msup> <i:mn>10</i:mn> <i:mn>15</i:mn> </i:msup> <i:mtext> </i:mtext> <i:mtext> </i:mtext> <i:mi>GeV</i:mi> </i:math> ), and beyond the Standard Model effective interaction scales spanning 11 orders of magnitude ( <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"> <k:msup> <k:mn>10</k:mn> <k:mn>3</k:mn> </k:msup> <k:mtext> </k:mtext> <k:mtext> </k:mtext> <k:mi>GeV</k:mi> <k:mo>≲</k:mo> <k:mi mathvariant="normal">Λ</k:mi> <k:mo>≲</k:mo> <k:msup> <k:mn>10</k:mn> <k:mn>14</k:mn> </k:msup> <k:mtext> </k:mtext> <k:mtext> </k:mtext> <k:mi>GeV</k:mi> </k:math> ), where a thermally averaged cross section has been parametrized as <n:math xmlns:n="http://www.w3.org/1998/Math/MathML" display="inline"> <n:mo stretchy="false">⟨</n:mo> <n:mi>σ</n:mi> <n:mi>v</n:mi> <n:mo stretchy="false">⟩</n:mo> <n:mo>=</n:mo> <n:mfrac> <n:msup> <n:mi>T</n:mi> <n:mi>n</n:mi> </n:msup> <n:msup> <n:mi mathvariant="normal">Λ</n:mi> <n:mrow> <n:mi>n</n:mi> <n:mo stretchy="false">+</n:mo> <n:mn>2</n:mn> </n:mrow> </n:msup> </n:mfrac> </n:math> . Interestingly, the most suitable range of couplings for UFO lies precisely between the typical couplings for WIMPs and FIMPs, rendering UFO quite attractive from the standpoint of detection. Particle physics models that are easily amenable to UFO include heavy vector or scalar portal interactions, along with nonrenormalizable effective interactions. Finally, we show there is a distinction between UV UFO and IR UFO, where the relic abundance for the former is sensitive to the freeze-out temperature, while the abundance for the latter is sensitive to the DM mass and the reheating temperature but insensitive to the freeze-out temperature.