The coincidence problem in $f(R)$ gravity models

Abstract

To explore possibilities of avoiding coincidence problem in $f(R)$ gravity we consider models in Einstein conformal frame which are equivalent to Einstein gravity with a minimally coupled scalar field. As the conformal factor determines the coupling term and hence the interaction between matter and dark energy, the function $f(R)$ can in principle be determined by choosing an appropriate function for the deceleration parameter only. Possible behavior of $f(R)$ to avoid coincidence problem are investigated in two such cases.

19 pages, 9 figures, Accepted for publication in General Relativity and Gravitation. arXiv admin note: substantial text overlap with arXiv:0807.1640 by other authors