Qualitative evolution in f(R) cosmologies
  We investigate the qualitative evolution of (D+1)-dimensional cosmological models in f(R) gravity for the general case of the function f(R). The analysis is specified for various examples, including the (D+1)-dimensional generalization of the Starobinsky model, models with polynomial and exponential functions. The cosmological dynamics are compared in the Einstein and Jordan representations of the corresponding scalar-tensor theory. The features of the cosmological evolution are discussed for Einstein frame potentials taking negative values in certain regions of the field space. 
R. M. Avagyan, E. V. Chubaryan, G. H. Harutyunyan, A. A. Saharian
gr-qc astro-ph.CO hep-th