Interacting dark energy in $f(R)$ gravity

Abstract

The field equations in $f(R)$ gravity derived from the Palatini variational principle and formulated in the Einstein conformal frame yield a cosmological term which varies with time. Moreover, they break the conservation of the energy--momentum tensor for matter, generating the interaction between matter and dark energy. Unlike phenomenological models of interacting dark energy, $f(R)$ gravity derives such an interaction from a covariant Lagrangian which is a function of a relativistically invariant quantity (the curvature scalar $R$). We derive the expressions for the quantities describing this interaction in terms of an arbitrary function $f(R)$, and examine how the simplest phenomenological models of a variable cosmological constant are related to $f(R)$ gravity. Particularly, we show that $\Lambda c^2=H^2(1-2q)$ for a flat, homogeneous and isotropic, pressureless universe. For the Lagrangian of form $R-1/R$, which is the simplest way of introducing current cosmic acceleration in $f(R)$ gravity, the predicted matter--dark energy interaction rate changes significantly in time, and its current value is relatively weak (on the order of 1% of $H_0$), in agreement with astronomical observations.

8 pages; published version

References in corpus (5)

• Cosmological viability of f(R)-gravity as an ideal fluid and its compatibility with a matter dominated phase
• Decaying Gravity
• Accelerated Cosmological Models in Modified Gravity tested by distant Supernovae SNIa data
• The cosmic jerk parameter in f(R) gravity
• An Interacting Dark Energy Model for the Expansion History of the Universe

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• f(R) gravity theories in Palatini formalism: cosmological dynamics and observational constraints
• Cosmological Constraints on f(R) Acceleration Models
• Violation of the Equivalence Principle in Modified Theories of Gravity
• Density perturbations in f(R) gravity theories in metric and Palatini formalisms
• The Cosmology of Ricci-Tensor-Squared Gravity in the Palatini Variational Approach
• Power-law cosmic expansion in f(R) gravity models
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• Accelerating Universe in Modified Theories of Gravity
• Dynamical systems analysis of anisotropic cosmologies in $R^n$-gravity
• The cosmic snap parameter in f(R) gravity
• Compactifying the state space for alternative theories of gravity
• Homogeneous cosmologies in generalized modified gravity