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The Standard Model (SM) of particle physics is an extremely successful theory that effectively describes strong and electroweak interactions up to the energies presently accessible. Still, the SM does not explain the observed parameters of neutrino oscillations, baryon asymmetry of the Universe and Dark Matter (DM), and contains a fine-tuning of 16 orders of magnitude (the gauge hierarchy problem). Various New Physics (NP) models beyond the SM have been developed in order to address the above limitations. This paper concentrates on several models related to cosmology and their tests in rare kaon decays. In particular, recent NA48/2 results on the search for heavy neutrinos, light in-flatons and dark photons are presented. Prospects for the ongoing NA62 experiment are discussed

Cosmology tests in rare kaon decays