I will discuss cosmic domain walls which are described by tension red-shifting with the expansion of the Universe so that this network eventually fades away completely. These melting domain walls emit gravitational waves with the low-frequency spectral shape corresponding to the spectral index γ=3 favoured by the recent NANOGrav 15 yrs data. This scenario involves a feebly coupled scalar field, which can serve as a promising dark matter candidate. This ultra-light dark matter has mass below 0.01 neV which is accessible through planned observations thanks to the effects of superradiance of rotating black holes. This talk is based on recent works: arXiv:2104.13722, arXiv:2112.12608, arXiv:2307.04582 and arXiv: 2406.17053.

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Professor Alexander Vikman is a senior permanent staff researcher at CEICO, Institute of Physics of the Czech Academy of Sciences, since 2015. Before that, he was Senior Research Assistant at Ludwig Maximilian University of Munich in Germany, CERN Fellow in Switzerland and James Arthur Postdoctoral Fellow at CCPP, New York University, USA. He has diverse interests in theoretical physics with a focus on deep and fundamental problems, especially for modified gravity, dark energy and studies of cosmological singularity at the origin of the universe. In particular, his works with coauthors on Covariant Galileons, systems with Kinetic Gravity Braiding and G Bounce became rather influential. He is also interested in dark matter and new ways of detecting its traces, including observations of gravitational waves.

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