Classifying and avoiding singularities in the alternative gravity dark
  energy models
  The future finite-time singularities emerging in alternative gravity dark
energy models are classified and studied in Jordan and Einstein frames. It is
shown that such singularity may occur even in flat spacetime for the specific
choice of the effective potential. The conditions for the avoidance of
finite-time singularities are presented and discussed. The problem is reduced
to the study of a scalar field evolving on an effective potential by using the
conformal transformations. Some viable modified gravity models are analyzed in
detail and the way to cure singularity is considered by introducing the
higher-order curvature corrections. These results maybe relevant for the
resolution of the conjectured problem in the relativistic star formation in
such modified gravity where finite-time singularity is also manifested.
