Title: Starobinsky inflation as a guide to quantum gravity

Abstract: In 1980 Starobinsky showed that one-loop corrections to the stress-energy tensor due to conformal anomaly allow a cosmological solution describing a Universe that can start from a de Sitter phase.This was the first model ever proposed in which what was later called inflation could be realized. However, it was soon understood that the initial model by Starobinsky needed a very large number of new unknown matter fields in order to work. In fact, Starobinsky himself in 1985 proposed a simplified version of his model whose Lagrangian was given by Einstein-Hilbert plus a term quadratic in the Ricci scalar: this is what is now known as the Starobinsky model of inflation. In this new model there is no need to introduce new matter fields because the coefficient of the quadratic-curvature term is a free parameter independent of the number of matter fields and in principle can take on any large value. From a fundamental point of view, however, the Lagrangian R+R^2 is non-renormalizable when quantized in the QFT framework. In this talk I discuss a unique perturbative completion of the Starobinsky model known as Quadratic Gravity which consists in adding the Weyl square term to the Lagrangian. This theory is motivated by standard QFT principles and is strictly renormalizable like the other fundamental interactions of the Standard Model. I argue that, to our current understanding, Quadratic Gravity is more predictive than any other popular approach to quantum gravity.