To me, the most difficult thing is that the quanta of gravity must have spin 2 and be massless, and you can't construct a quantum field theory which is Lorentz-invariant and renormalizable. This is wienberg-witten theorem.
A grand unified theory is a theoretical framework that attempts to unify all of the known fundamental forces in the universe, specifically the strong, weak, and electromagnetic forces, into a single mathematical model. It aims to explain the fundamental structure of the universe and the interactions between all particles.
Quantum mechanics is a fundamental theory of nature that describes the behavior of particles at the microscopic level. It is an essential component of grand unified theories as it provides the mathematical framework for understanding the behavior of particles and their interactions within the unified theory.
One of the main challenges in developing a grand unified theory is the inability to experimentally test it at the energies required for unification. Additionally, there are still many unanswered questions in both quantum mechanics and particle physics that must be addressed in order to create a complete and accurate grand unified theory.
While there is currently no direct experimental evidence for grand unified theories, there have been some successes in experiments that indirectly support the idea. For example, the existence of neutrino oscillations and the idea of baryogenesis can be explained by some GUT models.
Yes, grand unified theories are often linked to theories of cosmic inflation and the Big Bang. These theories propose that the universe underwent a rapid expansion in its early stages, and a grand unified theory can help explain the fundamental forces and particles that were present during this time.