Dark matter generation from a dark sector

The nondetection of dark matter may be attributed to the dark matter residing in a darker hidden sector. We explore the possibility that a hidden sector produced through the freeze-in mechanism, can further generate an even more hidden sector via an additional freeze-in process. Such a two-step freeze-in process produces dark matter coupled weaker-than-ultraweakly to the standard model particles, and is thus referred to as the “darker matter.” To illustrate the two-step freeze-in process, we study a model featuring two <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>U</a:mi><a:mo stretchy="false">(</a:mo><a:mn>1</a:mn><a:mo stretchy="false">)</a:mo></a:math> hidden sectors. The first <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mi>U</e:mi><e:mo stretchy="false">(</e:mo><e:mn>1</e:mn><e:mo stretchy="false">)</e:mo></e:math> sector is directly coupled to the standard model with feeble interactions, while the second <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:mi>U</i:mi><i:mo stretchy="false">(</i:mo><i:mn>1</i:mn><i:mo stretchy="false">)</i:mo></i:math> sector is directly coupled to the first <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:mi>U</m:mi><m:mo stretchy="false">(</m:mo><m:mn>1</m:mn><m:mo stretchy="false">)</m:mo></m:math> sector and thus only indirectly to the standard model, rendering it darker. Remarkably, darker matter candidates residing in the second darker <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"><q:mi>U</q:mi><q:mo stretchy="false">(</q:mo><q:mn>1</q:mn><q:mo stretchy="false">)</q:mo></q:math> sector, generated from the two-step freeze-in process, can account for almost the entire observed dark matter relic density. The darker matter, interacted with standard model particles through ultraweak couplings, can exhibit velocity-dependent self-interacting cross sections, which potentially provides an explanation for addressing problems associated with cosmic small-scale structures. Additionally, the dark photon darker matter residing in the darker hidden sector can be responsible for the galactic 511 keV photon signal, consistent with various dark matter density profiles.