Notes on Born-Infeld-like modified gravity

Abstract

We investigate the modified $F(R)$ gravity theory with the function $F(R)=(1-\sqrt{1-2\lambda R-\sigma (\lambda R{)}^2})/\lambda$. The action is converted into Einstein$-$Hilbert action at small values of $\lambda$ and $\sigma$. The local tests give a bound on the parameters, $\lambda (1+\sigma )\le 2\times 10^{-6}$ cm${}^2$. The Jordan and Einstein frames are considered, the potential, and the mass of the scalar field were obtained. The constant curvature solutions of the model are found. It was demonstrated that the de Sitter space is unstable but a solution with zero Ricci scalar is stable. The cosmological parameters of the model are evaluated. Critical points of autonomous equations are obtained and described.

21 pages, 10 figures, added references, journal version, accepted for publication in Astrophys. Space Sci

References in corpus (15)

• f(R,T) gravity
• Models of f(R) Cosmic Acceleration that Evade Solar-System Tests
• Disappearing cosmological constant in f(R) gravity
• Tests of the Gravitational Inverse-Square Law below the Dark-Energy Length Scale
• Conditions for the cosmological viability of f(R) dark energy models
• Dynamical Instability and Expansion-free Condition in $f(R,T)$ Gravity
• On the 1/c Expansion of f(R) Gravity
• Unitarity analysis of general Born-Infeld gravity theories
• Weak-field limit of f(R)-gravity in three and more spatial dimensions
• Reconstructing QCD ghost $f(R,T)$ models
• n-DBI gravity
• Born - Infeld-like modified gravity
• A Born-Infeld-like f(R) gravity
• A new $F(R)$-gravity model
• A Note on de Sitter Embedding of $f(R)$ Theories

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• Nonlinear Electromagnetic Fields As a Source of Universe Acceleration
• Beyond Starobinsky inflation
• Geodesically complete BTZ-type solutions of $2+1$ Born-Infeld gravity
• Logarithmic gravity model
• Born - Infeld-type modified gravity