The most general fourth order theory of Gravity at low energy

Abstract

The Newtonian limit of the most general fourth order gravity is performed with metric approach in the Jordan frame with no gauge condition. The most general theory with fourth order differential equations is obtained by generalizing the $f(R)$ term in the action with a generic function containing other two curvature invariants: \emph{Ricci square} ($R_{\alpha \beta }{R}^{\alpha \beta }$) and \emph{Riemann square} ($R_{\alpha \beta \gamma \delta }{R}^{\alpha \beta \gamma \delta }$). The spherically symmetric solutions of metric tensor yet present Yukawa-like spatial behavior, but now one has two characteristic lengths. At Newtonian order any function of curvature invariants gives us the same outcome like the so-called \emph{Quadratic Lagrangian} of Gravity. From Gauss - Bonnet invariant one have the complete interpretation of solutions and the absence of a possible third characteristic length linked to Riemann square contribution. From analysis of metric potentials, generated by point-like source, one has a constraint condition on the derivatives of $f$ with respect to scalar invariants.

7 pages, 2 figures

References in corpus (8)

• Wilkinson Microwave Anisotropy Probe (WMAP) Three Year Results: Implications for Cosmology
• Extra force in $f(R)$ modified theories of gravity
• Limit to General Relativity in f(R) theories of gravity
• The Newtonian Limit of F(R) gravity
• Spherical symmetry in $f(R)$-gravity
• The Parameterised Post-Newtonian Limit of Fourth-Order Theories of Gravity
• A general solution in the Newtonian limit of f(R)- gravity
• The Newtonian limit of metric gravity theories with quadratic Lagrangians

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