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In 2023, pulsar timing arrays (PTAs) announced the first detection of a gravitational wave background, marking the beginning of gravitational wave cosmology. One compelling explanation for this signal are strong first-order phase transitions in dark sectors beyond the Standard Model. This talk, aimed at non-experts in cosmology, provides an overview of the current status and future prospects of gravitational wave science at the nano-Hertz scale. Specifically, I will discuss how a phase transition occurring before the formation of the first elements in the early universe could simultaneously account for the observed dark matter abundance, explain the PTA signal, and lead to testable signatures in laboratory experiments. Before concluding, I will broaden the perspective by discussing how future gravitational wave observations, such as those from LISA, can provide insights into Higgs and dark matter physics at and beyond the electroweak scale—offering a complementary approach to particle colliders. The primary aim of this talk is to introduce myself and my research to the Uppsala group, fostering collaboration on these exciting questions in fundamental physics.