Abstract
In this paper, we investigate chaotic inflation from a scalar field subjected to a 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 $$e$$ -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.
Highlights
The paper is organized in the following way
In the framework of General Relativity they lead to a viable approach to inflation, and we are interested to see how results change for some toy model of Gauss–Bonnet modified gravity and a model based on the power-law functions of the curvature invariants under investigation
We have investigated chaotic inflation with a scalar field subjected to a potential in the framework of f (R2, P, Q)-modified gravity, namely the gravitational action of the theory includes a correction based on an function of the square of the Ricci scalar R2 and the contractions of the Ricci (P) and Riemann (Q) tensors
Summary
Where M is the space-time manifold, g is the determinant of the metric tensor gμν, and R is the Ricci scalar. The curvature invariants of the model on flat FRW space-time read. The dot denotes the derivative with respect to the time. By plugging these expressions into the action (1), we obtain a higher derivative Lagrangian. We obtained a first order Lagrangian with respect to the unknown variables N (t), a(t), R(t) ≡ R, P(t) ≡ P, Q(t) ≡ Q. Where the second expression is the form of the Gauss–Bonnet on the flat FRW space-time. To pass from f (R2, P, Q) to f (R, G)-gravity on the FRW space-time, we can substitute R2, P, Q with R2, G, C2 into the action (1). Let us see how the inflationary cosmology is reproduced by such a kind of models
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