Ping Xi, Xiang-hua Zhai, Xin-zhou Li
Depending on the choice of its potential, the scalar phantom field $\phi$
(the equation of state parameter $w<-1$) leads to various catastrophic fates of
the universe including big rip, little rip and other future singularity. For
example, big rip results from the evolution of the phantom field with an
exponential potential and little rip stems from a quadratic potential in
general relativity (GR). By choosing the same potential as in GR, we suggest a
new mechanism to avoid these unexpected fates (big and little rip) in the
inverse-\textit{R} gravity. As a pedagogical illustration, we give an exact
solution where phantom field leads to a power-law evolution of the scale factor
in an exponential type potential. We also find the sufficient condition for a
universe in which the equation of state parameter crosses $w=-1$ divide. The
phantom field with different potentials, including quadratic, cubic, quantic,
exponential and logarithmic potentials are studied via numerical calculation in
the inverse-\textit{R} gravity with $R^{2}$ correction. The singularity is
avoidable under all these potentials. Hence, we conclude that the avoidance of
big or little rip is hardly dependent on special potential.
View original:
http://arxiv.org/abs/1111.6355
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