Aspects of gravitational portals and freeze-in during reheating

We conduct a systematic investigation of freeze-in during reheating while taking care to include both direct and indirect production of dark matter (DM) via gravitational portals and inflaton decay. Direct production of DM can occur via gravitational scattering of the inflaton, while indirect production occurs through scattering in the Standard Model radiation bath. We consider two main contributions to the radiation bath during reheating. The first, which may dominate at the onset of the reheating process, is produced via gravitational scattering of the inflaton. The second (and more standard contribution) comes from inflaton decay. We consider a broad class of DM production rates parametrized as <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:msub><a:mi>R</a:mi><a:mi>χ</a:mi></a:msub><a:mo>∝</a:mo><a:msup><a:mi>T</a:mi><a:mrow><a:mi>n</a:mi><a:mo>+</a:mo><a:mn>6</a:mn></a:mrow></a:msup><a:mo>/</a:mo><a:msup><a:mi mathvariant="normal">Λ</a:mi><a:mrow><a:mi>n</a:mi><a:mo>+</a:mo><a:mn>2</a:mn></a:mrow></a:msup></a:math>, and inflaton potentials with a power-law form <d:math xmlns:d="http://www.w3.org/1998/Math/MathML" display="inline"><d:mi>V</d:mi><d:mo stretchy="false">(</d:mo><d:mi>ϕ</d:mi><d:mo stretchy="false">)</d:mo><d:mo>∝</d:mo><d:msup><d:mi>ϕ</d:mi><d:mi>k</d:mi></d:msup></d:math> about the minimum. We find the relic density produced by freeze-in for each contribution to the Standard Model bath for arbitrary <h:math xmlns:h="http://www.w3.org/1998/Math/MathML" display="inline"><h:mi>k</h:mi></h:math> and <j:math xmlns:j="http://www.w3.org/1998/Math/MathML" display="inline"><j:mi>n</j:mi></j:math>, and compare these with the DM density produced gravitationally by inflaton scattering. We find that freeze-in production from the gravitationally produced radiation bath can exceed that of the conventional decay bath and account for the observed relic density provided that <l:math xmlns:l="http://www.w3.org/1998/Math/MathML" display="inline"><l:msub><l:mi>m</l:mi><l:mi>χ</l:mi></l:msub><l:mo>&gt;</l:mo><l:msub><l:mi>T</l:mi><l:mrow><l:mi>RH</l:mi></l:mrow></l:msub></l:math>, with additional <n:math xmlns:n="http://www.w3.org/1998/Math/MathML" display="inline"><n:mi>k</n:mi></n:math>- and <p:math xmlns:p="http://www.w3.org/1998/Math/MathML" display="inline"><p:mi>n</p:mi></p:math>-dependent constraints. For each freeze-in interaction considered, we also find <r:math xmlns:r="http://www.w3.org/1998/Math/MathML" display="inline"><r:msub><r:mi>m</r:mi><r:mi>χ</r:mi></r:msub></r:math>- and <t:math xmlns:t="http://www.w3.org/1998/Math/MathML" display="inline"><t:msub><t:mi>T</t:mi><t:mrow><t:mi>RH</t:mi></t:mrow></t:msub></t:math>-dependent limits on the beyond the Standard Model scale, <v:math xmlns:v="http://www.w3.org/1998/Math/MathML" display="inline"><v:mi mathvariant="normal">Λ</v:mi></v:math>, for which gravitational production will exceed ordinary freeze-in production.