Energy Conditions and Stability in generalized $f(R)$ gravity with arbitrary coupling between matter and geometry

Abstract

The energy conditions and the Dolgov-Kawasaki criterion in generalized $f(R)$ gravity with arbitrary coupling between matter and geometry are derived in this paper, which are quite general and can degenerate to the well-known energy conditions in GR and $f(R)$ gravity with non-minimal coupling and non-coupling as special cases. In order to get some insight on the meaning of these energy conditions and the Dolgov- Kawasaki criterion, we apply them to a class of models in the FRW cosmology and give some corresponding results.

12 pages. arXiv admin note: substantial text overlap with arXiv:1203.5593, arXiv:1212.4656

References in corpus (18)

• Observational Evidence from Supernovae for an Accelerating Universe and a Cosmological Constant
• Measurements of Omega and Lambda from 42 High-Redshift Supernovae
• Five-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation
• 4D Gravity on a Brane in 5D Minkowski Space
• Relativistic gravitation theory for the MOND paradigm
• Curvature Quintessence
• Gravity with a dynamical preferred frame
• Brane-world gravity
• Can modified gravity explain accelerated cosmic expansion?
• Jerk, snap, and the cosmological equation of state
• Action functionals for relativistic perfect fluids
• Cosmography: Cosmology without the Einstein equations
• A kinematical approach to dark energy studies
• Matter instability in modified gravity
• A viability criterion for modified gravity with an extra force
• Constraining f(R) theories with the energy conditions
• Strong Energy Condition in $R+R^2$ Gravity
• $R+R^2$ Gravity as $R+$ Backreaction

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