Generalized virial theorem in Palatini $f(R)$ gravity

Abstract

We use the collision-free Boltzmann equation in Palatini $f(\mathcal{R})$ gravity to derive the virial theorem within the context of the Palatini approach. It is shown that the virial mass is proportional to certain geometrical terms appearing in the Einstein field equations which contribute to gravitational energy and that such geometric mass can be attributed to the virial mass discrepancy in cluster of galaxies. We then derive the velocity dispersion relation for clusters followed by the metric tensor components inside the cluster as well as the $f(\mathcal{R})$ lagrangian in terms of the observational parameters. Since these quantities may also be obtained experimentally, the $f(\mathcal{R})$ virial theorem is a convenient tool to test the viability of $f(\mathcal{R})$ theories in different models. Finally, we discuss the limitations of our approach in the light of the cosmological averaging used and questions that have been raised in the literature against such averaging procedures in the context of the present work.

16 pages, to appear in PRD

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Cited by in corpus (18)

• Palatini Approach to Modified Gravity: f(R) Theories and Beyond
• The virial theorem and the dark matter problem in hybrid metric-Palatini gravity
• Palatini formulation of modified gravity with a nonminimal curvature-matter coupling
• Hamiltonian Formulation of Palatini f(R) theories a la Brans-Dicke
• Palatini formulation of the conformally invariant $f\left(R,L_m\right)$ gravity theory
• Slowly rotating Bose Einstein Condensate galactic dark matter halos, and their rotation curves
• Testing Bose-Einstein Condensate dark matter models with the SPARC galactic rotation curves data
• Jeans instability and turbulent gravitational collapse of Bose-Einstein Condensate dark matter halos
• Brane-$f(R)$ gravity and dark matter
• Linearized physics and gravitational-waves polarizations in the Palatini formalism of GBD theory
• The virial theorem in Eddington-Born-Infeld gravity
• Bose-Einstein Condensate dark matter models in the presence of baryonic matter and random confining potentials
• f(T) Quantum Cosmology
• Spherical collapse and virialization in $f(T)$ gravities
• Velocity and velocity bounds in static spherically symmetric metrics
• Generalized virial theorem in warped DGP brane-world
• Quantum cosmology in teleparallel gravity with a boundary term
• Stable massless scalar polarization of f(R) gravity