The spontaneous production of particles due to a gravitational field is one of the cornerstones of the theory of quantum fields in curved spacetime. This effect has an important role in our current understanding of the early phases of the Universe. I will introduce this phenomenon and point out the difficulties that arise when computing physical magnitudes, e.g. the stress-energy tensor. I will show how we can overcome these issues and how to generalize this description to interacting fields, e.g., to understand the generation of matter during the reheating phase in the inflationary scenario.
Adrian del Rio