Notions of affinity in calculus of variations with differential forms

Ext-int.\ one affine functions are functions affine in the direction of one-divisible exterior forms, with respect to exterior product in one variable and with respect to interior product in the other. The purpose of this article is to prove a characterization theorem for this class of functions, which plays an important role in the calculus of variations for differential forms

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

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