# Phantom behaviour and growth index anomalous evolution in viable f ( R ) gravity models 

Hayato Motohashi ∗ ( a ) , ( b ) , Alexei A. Starobinsky † ( b ) , ( c ) and Jun’ichi Yokoyama ‡ ( b ) , ( d ) 

( a ) Department of Physics, Graduate School of Science, The University of Tokyo, Tokyo 113-0033, Japan 

( b ) Research Center for the Early Universe (RESCEU), Graduate School of Science, The University of Tokyo, Tokyo 113-0033, Japan 

( c ) L. D. Landau Institute for Theoretical Physics, Moscow 119334, Russia 

( d ) Institute for the Physics and Mathematics of the Universe(IPMU), The University of Tokyo, Kashiwa, Chiba, 277-8568, Japan 

## Abstract 

We present numerical calculation of the evolution of a background space-time metric and sub- horizon matter density perturbations in viable f ( R ) gravity models of present dark energy and cosmic acceleration. We found that viable models generically exhibit recent crossing of the phantom boundary w$_{DE}$ = − 1. Moreover, as a consequence of the anomalous growth of density perturbations during the end of the matter-dominated stage, their growth index evolves non-monotonically with time and may even become negative. 

