Chaotic inflation in higher derivative gravity theories

In this paper, we investigate chaotic inflation from a scalar field subjected to a potential in the framework of $$f(R^2, P, Q)$$f(R2,P,Q)-gravity, where we add a correction to Einstein’s gravity based on a function of the square of the Ricci scalar $$R^2$$R2, the contraction of the Ricci tensor $$P$$P, and the contraction of the Riemann tensor $$Q$$Q. The Gauss–Bonnet case is also discussed. We give the general formalism of inflation, deriving the slow-roll parameters, the $$e$$e-fold number, and the spectral indices. Several explicit examples are furnished; namely, we will consider the cases of a massive scalar field and a scalar field with quartic potential and some power-law function of the curvature invariants under investigation in the gravitational action of the theory. A viable approach to inflation according with observations is analyzed.