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The cosmological reconstruction of the Little Rip model in f (R, T) gravity is investigated, where R is the curvature scalar and T the trace of the energy momentum tensor. The model perfectly reproduces the present stage of the universe, characterized by the \( \Lambda\) CDM model, without singularity at future finite-time (without the Big Rip). The input parameters are determined according to Supernovae cosmology data and perfectly fit with the WMAP around the Little Rip. Moreover, the thermodynamics is considered in this Little Rip cosmology and it is illustrated that the second law of thermodynamics is always satisfied around the Little Rip universe for the temperature inside the horizon being the same as that of the apparent horizon. Moreover, we show the existence of a stable fixed point in the Little Rip universe which confirms that this is actually a late-time attractor in the phantom-dominated universe. The linear perturbation analysis is performed around the critical points, showing that the Little Rip model obtained is stable.

Thermodynamics in Little Rip cosmology in the framework of a type of f(R, T) gravity