Inflaton production of scalar dark matter through fluctuations and scattering

We study the effects on particle production of a Planck-suppressed coupling between the inflaton and a scalar dark matter candidate, <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>χ</a:mi></a:math>. In the absence of this coupling the dominant source for the relic density of <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mi>χ</c:mi></c:math> is the long wavelength modes produced from the scalar field fluctuations during inflation. In this case, there are strong constraints on the mass of the scalar and the reheating temperature after inflation from the present-day relic density of <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mi>χ</e:mi></e:math> (assuming <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:mi>χ</g:mi></g:math> is stable). When a coupling <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:mi>σ</i:mi><i:msup><i:mi>ϕ</i:mi><i:mn>2</i:mn></i:msup><i:msup><i:mi>χ</i:mi><i:mn>2</i:mn></i:msup></i:math> is introduced, with <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:mi>σ</k:mi><k:mo>=</k:mo><k:mover accent="true"><k:mi>σ</k:mi><k:mo stretchy="false">˜</k:mo></k:mover><k:msubsup><k:mi>m</k:mi><k:mi>ϕ</k:mi><k:mn>2</k:mn></k:msubsup><k:mo>/</k:mo><k:msubsup><k:mi>M</k:mi><k:mi>P</k:mi><k:mn>2</k:mn></k:msubsup><k:mo>∼</k:mo><k:msup><k:mn>10</k:mn><k:mrow><k:mo>−</k:mo><k:mn>10</k:mn></k:mrow></k:msup><k:mover accent="true"><k:mi>σ</k:mi><k:mo stretchy="false">˜</k:mo></k:mover></k:math>, where <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"><q:msub><q:mi>m</q:mi><q:mi>ϕ</q:mi></q:msub></q:math> is the inflaton mass, the allowed parameter space begins to open up considerably even for <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"><s:mover accent="true"><s:mi>σ</s:mi><s:mo stretchy="false">˜</s:mo></s:mover></s:math> as small as <w:math xmlns:w="http://www.w3.org/1998/Math/MathML" display="inline"><w:mo>≳</w:mo><w:msup><w:mn>10</w:mn><w:mrow><w:mo>−</w:mo><w:mn>7</w:mn></w:mrow></w:msup></w:math>. For <y:math xmlns:y="http://www.w3.org/1998/Math/MathML" display="inline"><y:mover accent="true"><y:mi>σ</y:mi><y:mo stretchy="false">˜</y:mo></y:mover><y:mo>≳</y:mo><y:mfrac><y:mn>9</y:mn><y:mn>16</y:mn></y:mfrac></y:math>, particle production is dominated by the scattering of the inflaton condensate, either through single graviton exchange or the contact interaction between <cb:math xmlns:cb="http://www.w3.org/1998/Math/MathML" display="inline"><cb:mi>ϕ</cb:mi></cb:math> and <eb:math xmlns:eb="http://www.w3.org/1998/Math/MathML" display="inline"><eb:mi>χ</eb:mi></eb:math>. In this regime, the range of allowed masses and reheating temperatures is maximal. For <gb:math xmlns:gb="http://www.w3.org/1998/Math/MathML" display="inline"><gb:mn>0.004</gb:mn><gb:mo>&lt;</gb:mo><gb:mover accent="true"><gb:mi>σ</gb:mi><gb:mo stretchy="false">˜</gb:mo></gb:mover><gb:mo>&lt;</gb:mo><gb:mn>50</gb:mn></gb:math>, constraints from isocurvature fluctuations are satisfied, and the production from parametric resonance can be neglected. Published by the American Physical Society 2024