Chaotic inflation in higher derivative gravity theories

Abstract

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

19 pages, final version, accepted in EPJC

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• Scalar tensor Horndeski models: simple cosmological applications
• K-essence in Horndeski models
• $k$-essence non-minimally coupled with Gauss-Bonnet invariant for inflation
• Constraints on the Combined Models with $R^{2-q}$ Inflation and Viable $f(R)$ Dark Energy
• Classical and quantum cosmology of $K$-essentially modified $R^2$ and pure $R^p$ gravity
• Study of Some Chaotic Inflationary Models in f(R) Gravity