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28 March 2024
 
  » arxiv » 1108.1665

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Constraints on fourth order generalized f(R) gravity
Emilio Santos ;
Date 8 Aug 2011
AbstractA fourth order generalized f(R) gravity theory (FOG) is considered with the Einstein-Hilbert action $R+aR^{2}+bR_{mu u}R^{mu u},$ $R_{mu u}$ being Ricci’{}s tensor and R the curvature scalar. The field equations are applied to spherical bodies where Newtonian gravity is a good approximation. The result is that for $0leq asim -b<<R^{2}$, $R$ being the body radius, the gravitational field outside the body contains two Yukawas, one attractive and the other one repulsive, in addition to the Newtonian term. For $asim -b>>R^{2}$ the gravitational field near the body is zero but at distances greater than $sqrt{a}sim sqrt{-b}$ the field is practically Newtonian. From the comparison with laboratory experiments I conclude that $sqrt{a}$ and $sqrt{-b}$ should be smaller than a few millimeters, which excludes any relevant effect of FOG on stars, galaxies or cosmology.
Source arXiv, 1108.1665
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