Abstract
The fundamental problem of the occurrence/removal of finite-time future singularity in the universe evolution for coupled Dark Energy (DE) is addressed. It is demonstrated the existence of the (instable or local minimum) de Sitter space solution which may cure the Type II or Type IV future singularity for DE coupled with DM as the result of tuning the initial conditions. In case of phantom DE, the corresponding coupling may help to resolve the coincidence problem but not the Big Rip (Type I) singularity issue. We show that modified gravity of special form or inhomogeneous DE fluid may offer the universal scenario to cure the Type I, II, III or IV future singularity of coupled (fluid or scalar) DE evolution.
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