Newtonian, Post Newtonian and Parameterized Post Newtonian limits of f(R, G) gravity

Abstract

We discuss in detail the weak field limit of f(R,G) gravity taking into account analytic functions of the Ricci scalar R and the Gauss-Bonnet invariant G. Specifically, we develop, in metric formalism, the Newtonian, Post Newtonian and Parameterized Post Newtonian limits starting from general f(R, G) Lagrangian. The special cases of f(R) and f(G) gravities are considered. In the case of the Newtonian limit of f(R, G) gravity, a general solution in terms of Green's functions is achieved.

26 pages

References in corpus (14)

• Unified cosmic history in modified gravity: from F(R) theory to Lorentz non-invariant models
• Extended Theories of Gravity
• Extended Theories of Gravity and their Cosmological and Astrophysical Applications
• Dark energy in modified Gauss-Bonnet gravity: late-time acceleration and the hierarchy problem
• Towards singularity and ghost free theories of gravity
• Dark energy cosmology from higher-order, string-inspired gravity and its reconstruction
• Construction of cosmologically viable f(G) gravity models
• String-inspired Gauss-Bonnet gravity reconstructed from the universe expansion history and yielding the transition from matter dominance to dark energy
• The Newtonian Limit of F(R) gravity
• Ghosts, Instabilities, and Superluminal Propagation in Modified Gravity Models
• Ghost conditions for Gauss-Bonnet cosmologies
• Ghost Constraints on Modified Gravity
• A general solution in the Newtonian limit of f(R)- gravity
• Unsuccessful cosmology with Modified Gravity Models

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• Dawn of the dark: unified dark sectors and the EDGES Cosmic Dawn 21-cm signal
• f(G) Noether cosmology
• Noether Symmetries as a geometric criterion to select theories of gravity
• Regular black holes in $f(G)$ gravity
• Dynamical analysis on $f(R,\mathcal{G})$ cosmology
• Observational constraints on Gauss-Bonnet cosmology
• The gravitational energy-momentum pseudotensor: the cases of $f(R)$ and $f(T)$ gravity
• Cosmological perfect fluids in Gauss-Bonnet gravity
• Nonlocal Teleparallel Cosmology
• Noether Symmetry Approach for teleparallel-curvature cosmology
• Late-time constraints on modified Gauss-Bonnet cosmology
• Thermodynamical aspects of relativistic hydrodynamics in f(R,G) gravity
• Noether symmetries and boundary terms in extended Teleparallel gravity cosmology
• Tracing the cosmic history by Gauss-Bonnet gravity
• Accelerating bianchi type dark energy cosmological model with cosmic string in f(T) Gravity
• Weak field limit and gravitational waves in higher-order gravity
• Topological invariant quintessence
• Spherically symmetric solution of $f(R,\mathcal{G})$ gravity at low energy
• De Sitter and Power-law Solutions in Non-local Gauss-Bonnet Gravity
• Noether Symmetry Analysis of Anisotropic Universe in Modified Gravity
• Renormalizability of alternative theories of gravity: differences between power counting and entropy argument
• Impact of projective curvature tensor in $f\left(R,G\right)$, $f\left(R,T\right)$ and $f\left(R,L_m\right)$-gravity
• Constraints on a scalar-tensor model with Gauss-Bonnet coupling from SN Ia and BAO observations
• Generalized Noether Theorem for Gauss-Bonnet Cosmology