Inflationary gravitational waves and laboratory searches as complementary probes of right-handed neutrinos

We analyze the damping of inflationary gravitational waves (GW) that re-enter the Hubble horizon before or during a post inflationary era dominated by a metastable right-handed neutrino (RHN), whose out-of-equilibrium decay releases entropy. Within a minimal type-I seesaw extension of the Standard Model, we explore the conditions under which the population of thermally produced RHNs remain long-lived and cause a period of matter domination. We find that the suppression of the GW spectrum occurs above a characteristic frequency determined by the RHN mass and active-sterile mixing. For RHN masses in the range 0.1–10 GeV and mixing <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:msup><a:mn>10</a:mn><a:mrow><a:mo>−</a:mo><a:mn>12</a:mn></a:mrow></a:msup><a:mo>≲</a:mo><a:mo stretchy="false">|</a:mo><a:msub><a:mi>V</a:mi><a:mrow><a:mi>e</a:mi><a:mi>N</a:mi></a:mrow></a:msub><a:msup><a:mo stretchy="false">|</a:mo><a:mn>2</a:mn></a:msup><a:mo>≲</a:mo><a:msup><a:mn>10</a:mn><a:mrow><a:mo>−</a:mo><a:mn>5</a:mn></a:mrow></a:msup></a:math>, we estimate such characteristic frequencies and the signal-to-noise ratio to assess the detection prospects in GW observatories such as THEIA, <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mi>μ</e:mi></e:math>-ARES, LISA, BBO, and ET. Additionally we use LIGO data to put upper bounds on the reheating temperature after inflation, for a given blue-tilted GW spectrum. We find complementarity between GW signals and laboratory searches in SHiP, DUNE, and LEGEND-1000. Notably, RHN masses of 0.2–2 GeV and mixing <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>10</g:mn></g:mrow></g:msup><g:mo>≲</g:mo><g:mo stretchy="false">|</g:mo><g:msub><g:mi>V</g:mi><g:mrow><g:mi>e</g:mi><g:mi>N</g:mi></g:mrow></g:msub><g:msup><g:mo stretchy="false">|</g:mo><g:mn>2</g:mn></g:msup><g:mo>≲</g:mo><g:msup><g:mn>10</g:mn><g:mrow><g:mo>−</g:mo><g:mn>7</g:mn></g:mrow></g:msup></g:math> are testable in both laboratory experiments and GW observations. Additionally, GW experiments can probe the canonical seesaw regime of light neutrino mass generation, a region largely inaccessible to laboratory searches.