f(R) dual theories of quintessence: expansion-collapse duality

Abstract The accelerated expansion of the universe demands presence an exotic matter, namely dark energy. Though cosmological constant fits this role very well, a scalar field minimally coupled to gravity, or quintessence, can also be considered as viable alternative for constant. We study f ( R ) gravity models which lead effective description energy implemented by quintessence fields in Einstein using frame-Jordan frame duality. For family models, reconstruction function Jordan consists two parts. first obtain perturbative solution frame, applicable near present epoch. Second, we asymptotic ), consistent with late time limit if drives universe. show that certain class grows maximum finite size, after it begins collapse back. Thus, there is possibility where continues expand, collapses. condition expansion-collapse duality then generalized varying equations state taking into account non-relativistic matter any other component This mapping between expanding geometry and collapsing at equation level may have interesting potential implications on growth perturbations therein times.