Abstract
The field equations in 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, gravity derives such an interaction from a covariant Lagrangian which is a function of a relativistically invariant quantity (the curvature scalar ). We derive the expressions for the quantities describing this interaction in terms of an arbitrary function , and examine how the simplest phenomenological models of a variable cosmological constant are related to gravity. Particularly, we show that for a flat, homogeneous and isotropic, pressureless universe. For the Lagrangian of form , which is the simplest way of introducing current cosmic acceleration in 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 ), in agreement with astronomical observations.
- Received 27 July 2006
DOI:https://doi.org/10.1103/PhysRevD.74.084032
©2006 American Physical Society