Jumping from Metric f(R) to Scalar-Tensor Theories and the relations between their post-Newtonian Parameters

Abstract

We review the dynamical equivalence between $f(R)$ gravity in the metric formalism and scalar-tensor gravity, and use this equivalence to deduce the post-Newtonian parameters $\gamma$ and $\beta$ for a $f(R)$ theory, obtaining a result that is different with respect to that known in the literature. Then, we obtain explicit expressions of these paremeters in terms of the mass of the scalar field (or, differently speaking, the mass of the additional scalar degree of freedom associated to a $f(R)$ theory) which can be used to constrain $f(R)$ gravity by means of current observations.

10 pages, 1 table, no figures Accepted for publication in CQG

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• Black hole solutions in F(R) gravity with conformal anomaly
• Gravitational Wave Polarization Modes in $f(R)$ Theories
• Post-Newtonian parameters gamma and beta of scalar-tensor gravity with a general potential
• Gauge invariant formulation of gravitational waves in metric $f(R)$ gravity
• Constraints on Horndeski Theory Using the Observations of Nordtvedt Effect, Shapiro Time Delay and Binary Pulsars
• Dark matter admixed strange quark stars in the Starobinsky model
• Post-Newtonian parameters and cosmological constant of screened modified gravity
• Post-Newtonian parameter $\gamma$ for multiscalar-tensor gravity with a general potential
• Scalar modes in extended hybrid metric-Palatini gravity: weak field phenomenology
• Dark stars in Starobinsky's model
• Can the Big Bang Singularity be avoided by a single scalar field?
• Superradiant energy extraction from rotating hairy Horndeski black holes
• Generalized Ashtekar variables for Palatini f(R) models
• Solar System Constraints on Scalar Tensor Theories with Non-Standard Action
• Post-Newtonian $\gamma$-like parameters and the gravitational slip in scalar-tensor and $f(R)$ theories
• Equivalence between Scalar-Tensor theories and $f(R)$-gravity: From the action to Cosmological Perturbations
• Constraints on scalar-tensor theories of gravity from observations
• Constraining some $r^{-n}$ extra-potentials in modified gravity models with LAGEOS-type laser-ranged geodetic satellites
• A detailed first-order post-Newtonian analysis of massive Brans-Dicke theories: numerical constraints and the $\beta$ parameter meaning
• High frequency limit for gravitational perturbations of cosmological models in modified gravity theories
• BPS Skyrme neutron stars in generalized gravity
• Conformal Frame dependence on Cosmological Observations in Scalar-Tensor Theories of Gravity
• Conformal coupling associated with the Noether symmetry and its connection with the $\Lambda$CDM dynamics