Complementarity between cosmic string gravitational waves and long-lived particle searches in a laboratory

Cosmic strings are powerful witnesses to cosmic events including any period of early matter domination. If such a period of matter domination was catalyzed by metastable, long-lived particles, then there will be complementary signals to ascertain the nature of the dark sector in experiments detecting primordial features in the gravitational wave (GW) power spectrum and laboratory searches for long-lived particles. We give explicit examples of global and local <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> gauge extended dark sectors to demonstrate such a complementarity as the union of the two experiments reveals more information about the dark sector than either experiment. Demanding that Higgs-portal long-lived scalar be looked for, in various experiments such as DUNE, FASER, FASER-II, MATHUSLA, and SHiP, we identify the parameter space that leads to complementary observables for GW detectors such as the Laser Interferometer Space Antenna and Einstein Telescope.