Planck-scale violations of Lorentz symmetries and their implications for astrophysics and cosmology

The Planck energy is generally considered to be the scale where quantum gravitational effects become important. In this talk, I will illustrate some of the most relevant features of models where the Planck scale governs deformations of relativistic symmetries. I will then discuss opportunities for experimental tests of such models arising in physical frameworks much below the Planck scale. This concerns some astrophysical observations, sensitive to tiny residual signatures at low energies thanks to amplification mechanisms, and cosmological observations carrying information about primordial perturbations in the early universe, which are directly influenced by Planck-scale physics. If time allows, I will comment on some recent developments on the implications of Planck-scale-deformed symmetries for the decoherence of quantum systems.