Inflationary gravitational wave spectral shapes as a test for low-scale leptogenesis

We study nonthermal resonant leptogenesis in a general setting, where a heavy Majoron <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mi>ϕ</a:mi> </a:math> decays to right-handed neutrinos (RHNs) whose further out-of-equilibrium decay generates the required lepton asymmetry. Domination of the energy budget of the Universe by the <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:mi>ϕ</c:mi> </c:math> or the RHNs alters the evolution history of the primordial gravitational waves (GWs) of inflationary origin, which re-enter the horizon after inflation, modifying the spectral shape. The decays of <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:mi>ϕ</e:mi> </e:math> and RHNs release entropy into the early Universe, while nearly degenerate RHNs facilitate low- and intermediate-scale leptogenesis. A characteristic damping of the GW spectrum resulting in kneelike features would provide evidence for low-scale nonthermal leptogenesis. We explore the parameter space for the lightest right-handed neutrino mass <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"> <g:msub> <g:mi>M</g:mi> <g:mn>1</g:mn> </g:msub> <g:mo>∈</g:mo> <g:mo stretchy="false">[</g:mo> <g:msup> <g:mn>10</g:mn> <g:mn>2</g:mn> </g:msup> <g:mo>,</g:mo> <g:msup> <g:mn>10</g:mn> <g:mn>14</g:mn> </g:msup> <g:mo stretchy="false">]</g:mo> <g:mtext> </g:mtext> <g:mtext> </g:mtext> <g:mi>GeV</g:mi> </g:math> and washout parameter <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"> <k:mi>K</k:mi> </k:math> that depends on the light-heavy neutrino Yukawa couplings <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"> <m:mi>λ</m:mi> </m:math> , in the weak ( <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"> <o:mi>K</o:mi> <o:mo><</o:mo> <o:mn>1</o:mn> </o:math> ) and strong ( <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"> <q:mi>K</q:mi> <q:mo>></q:mo> <q:mn>1</q:mn> </q:math> ) washout regimes. The resulting novel features compatible with observed baryon asymmetry are detectable by future experiments, like LISA and Einstein Telescope. By estimating the signal-to-noise ratio for upcoming GW experiments, we investigate the effect of the Majoron mass <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"> <s:msub> <s:mi>M</s:mi> <s:mi>ϕ</s:mi> </s:msub> </s:math> and reheating temperature <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"> <u:msub> <u:mi>T</u:mi> <u:mi>ϕ</u:mi> </u:msub> </u:math> , which depends on the <w:math xmlns:w="http://www.w3.org/1998/Math/MathML" display="inline"> <w:mi>ϕ</w:mi> <w:mo>−</w:mo> <w:mi>N</w:mi> </w:math> Yukawa couplings <y:math xmlns:y="http://www.w3.org/1998/Math/MathML" display="inline"> <y:msub> <y:mi>y</y:mi> <y:mi>N</y:mi> </y:msub> </y:math> .