On exponential modified gravity

Abstract

A modified theory of gravity with the function $F(R)=R\exp (\alpha R)$ instead of Ricci scalar $R$ in the Einstein$-$Hilbert action is considered and analyzed. The action of the model is converted into Einstein$-$Hilbert action at small value of the parameter $\alpha$. From local tests we obtain a bound on the parameter $\alpha \le 10^{-6}$ cm${}^2$. The Jordan and Einstein frames are investigated and the potential of the scalar field in Einstein's frame is found. The mass of a scalar degree of freedom as a function of curvature is obtained. The static solutions of the model are found corresponding to the Schwarzschild$-$de Sitter space. We show that the de Sitter space is unstable but a solution with zero curvature is stable. The cosmological parameters of the model are calculated. It was demonstrated that the model passes the matter stability test.

20 pages, 9 figures, changed title, extended version, added a section, figures and references, to be published in IJMPA

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• Modified arctan-gravity model mimicking a cosmological constant
• Logarithmic corrected $F(R)$ gravity in the light of Planck 2015
• Dynamical properties of Bianchi-I spacetimes in $f(R)$ gravity
• A new $F(R)$-gravity model
• Logarithmic gravity model
• A new model of arcsin-gravity
• Born - Infeld-type modified gravity
• On Pseudo $B$-symmetric spacetimes and $f(\mathcal{R})$ gravity
• A Note on Gravitational Memory in F(R)-theories and their Equivalent Scalar-Tensor Theories