One-loop modified gravity in a 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, φ) of the Ricci scalar R, the kinetic term K of a scalar field φ. 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 σ error range of the BICEP2 result.

Non-minimal two-loop inflation

“…We show the concrete expressions for the scalar fluctuations, the spectral index and the tensor-to-scalar ratio at the two loop level in Section 3. The Lyapunov stability of de Sitter solutions is studied in Section 4 in close analogy with the corresponding study for log-corrected higher-derivative quantum gravity [28]. In Section 5, we numerically evaluate the inflationary parameters and show possible parameters consistent with the observed data.…”

Inflationary Cosmology in Modified Gravity Theories

“…Various descriptions of inflationary models in terms of scalar field models [53] and perfect fluid as well as F (R) gravity [54] have been examined. Moreover, the effects of quantum corrections on inflation have been explored in References [55][56][57]. We note that the BICEP2 experiment has recently detected the B-mode polarization of the cosmic microwave background (CMB) radiation with the tensor to scalar ratio r = 0.20…”

Trace-anomaly driven inflation in f(T) gravity with a cosmological constant

“…Such theory is well posed as teleparallel equivalence of gravity (TEGR) and is inspired by f (R) gravity. People started to work on f (T ) gravity in the attempt to reproduce accelerated cosmology (Buchbinder et al 1992;Mukhanov and Winitzki 2007;Bamba et al 2010Bamba et al , 2011Bamba et al , 2012aBamba et al , 2013aBamba et al , 2014aBamba et al , 2014bOdintsov 2013, 2014;Amoros et al 2013Amoros et al , 2014Jamil et al 2012aJamil et al , 2012bJamil et al , 2012cJamil et al , 2013Momeni and Gholizade 2009;Momeni 2011;Bengochea and Ferraro 2009;Linder 2010aLinder , 2010bWu and Yu 2011;Geng et al 2011). For inflation see Fiorini (2007, 2008); Chen et al (2011); Wu and Geng (2012); Izumi et al (2014); Li et al (2011); Geng et al (2011Geng et al ( , 2013Geng et al ( , 2012; Xu et al (2012); Ong et al (2013); Izumi and Ong (2013); Yang (2011); Bamba et al (2012bBamba et al ( , 2013bBamba et al ( , 2014c; Basilakos et al (2013); De Haro and Amoros (2013).…”