Both Einstein's equations and the field equations of a modified theory of gravity can be derived as equations of state from purely thermodynamical considerations, leading to the identification of GR with an equilibrium state of gravity and modified gravity with a non-equilibrium one. This breakthrough made the relationship between gravity and thermodynamics even more intriguing. I will present a new approach to the thermodynamics of modified gravity which is inspired by these results, but follows a starkly different path.

Hořava-Lifshitz gravity has been proposed as a ghost-free and renormalizable quantum gravity model candidate with an anisotropic UV-scaling between space and time. In my talk I would like to present a cosmological background analysis of two different formulations of the theory, with particular focus on the running of the parameter λ with energy.

The problem of identification of ultra-high-energy cosmic ray (UHECR) sources is greatly complicated by the fact that even the highest energy cosmic rays may be deflected by tens of degrees in the galactic magnetic fields. We show that arrival directions of UHECRs from several nearest active galaxies form specific patterns in the sky, which can be effectively recognized by convolutional neural networks.

Supermassive black holes power accretion flows and outflows, and resulting radiation is observed at different wavelengths. A significant energy fraction of these flows may be carried by cosmic rays and associated high-energy non-thermal radiations. Recently, associations of high-energy neutrinos with galaxies hosting supermassive black holes, active galactic nuclei and tidal disruption events, have been reported. We review the implications of the multimessenger data for theoretical models and discuss their challenges.