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Where will Einstein fail? Lessons for gravity and cosmology

Einstein's theory of General Relativity is the benchmark example for empirical success and mathematical elegance in theoretical physics. However, in spite of being the most successfully tested theory in physics, there are strong theoretical and observational arguments for why General Relativity should fail. It is not a question of if, but rather a question of where and when! I start by recounting the tremendous success in observational cosmology over the past three decades, that has led to the era of precision cosmology. I will then summarize the pathologies in Einstein's theory of gravity, as the cornerstone of standard cosmological model. Attempts to address these pathologies are either inspired by mathematical elegance, or empirical falsifiability. Here, I provide different arguments for why a falsifiable solution should violate Lorentz symmetry, or revive "gravitational aether". Deviations from Einstein's gravity are then expected in: 1) cosmological matter-radiation transition, 2) neutron stars, 3) gravitomagnetic effect, 4) astrophysical black holes, and their potential connection to dark energy, and 5) early Universe, where the predictions are ranked by their degree of robustness and falsifiability.