Modified arctan-gravity model mimicking a cosmological constant

Abstract

A novel theory of $F(R)$ gravity with the Lagrangian density $\mathcal{L}=[R-(b/\beta )\arctan \left(\beta R\right)]/(2{\kappa }^2)$ is analyzed. Constant curvature solutions of the model are found, and the potential of the scalar field and the mass of a scalar degree of freedom in Einstein's frame are derived. The cosmological parameters of the model are calculated, which are in agreement with the PLANCK data. Critical points for the de Sitter phase and the matter dominated epoch of autonomous equations are obtained and studied.

8 pages, 8 figures, minor corrections, journal version

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• Nonlinear Electromagnetic Fields As a Source of Universe Acceleration
• Electromagnetic Structure of Few-Nucleon Ground States
• Born-Infeld-$f(R)$ gravity
• The long and winding road from chiral effective Lagrangians to nuclear structure
• Little Rip, $\Lambda$CDM and singular dark energy cosmology from Born-Infeld-$f(R)$ gravity
• Cascading dust inflation in Born-Infeld gravity
• Logarithmic corrected $F(R)$ gravity in the light of Planck 2015
• Nonsingular black holes in Palatini extensions of General Relativity
• Anisotropic Born-Infeld-f(R) Cosmologies
• A new $F(R)$-gravity model
• Cosmology of unimodular Born-Infeld-$f(R)$ gravity
• Viability of Arctan Model of f(R) Gravity for Late-time Cosmology
• Logarithmic gravity model
• A new model of arcsin-gravity
• A New f(R) Model in the Light of Local Gravity Test and Late-time Cosmology
• Born-Infeld-f(R) black holes