One-loop Modified Gravity in de Sitter Universe, Quantum Corrected Inflation, and its Confrontation with the Planck Result

Abstract

Motivated by issues on inflation, a generalized modified gravity model is investigated, where the model Lagrangian is described by a smooth function $f(R,K,\varphi )$ of the Ricci scalar $R$, the kinetic term $K$ of a scalar field $\varphi$. In particular, the one-loop effective action in the de Sitter background is examined on-shell as well as off-shell in the Landau gauge. In addition, the on-shell quantum equivalence of $f(R)$ gravity in the Jordan and Einstein frames is explicitly demonstrated. Furthermore, we present applications related to the stability of the de Sitter solutions and the one-loop quantum correction to inflation in quantum-corrected $R^2$ gravity. It is shown that for a certain range of parameters, the spectral index of the curvature perturbations can be consistent with the Planck analysis, but the tensor-to-scalar ratio is smaller than the minimum value within the 1 $\sigma$ error range of the BICEP2 result.

21 pages, no figure, several references added

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Cited by in corpus (19)

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• Mimetic gravity: a review of recent developments and applications to cosmology and astrophysics
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• Predictions on mass of Higgs portal scalar dark matter from Higgs inflation and flat potential
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• f(R) and Brans-Dicke Theories and the Swampland
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• $\infty -\infty$: vacuum energy and virtual black-holes
• Darkflation -- one scalar to rule them all?
• Cosmological Issues in $F(T)$ Gravity Theory
• Logarithmic curvature correction to Lifshitz and hyperscaling violation geometries