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A spatially flat Friedmann universe filled with two interacting ideal fluids (dark energy and dark matter) is considered. The gravitational equations of motion are solved with allowance for the interaction between dark energy and dark matter. It is shown that a periodic universe can form with cosmological singularities, it becomes static in the infinitely distant future.
A spatially flat Friedmann model of the Universe filled with the perfect liquid with a nonlinear homogeneous time-dependent equation of state is discussed. A gravitational equation of motion is solved. It is shown that in this case, there can result a periodic Universe rerunning cycles of space acceleration of the phantom (non-phantom) type with occurrence of cosmological singularities.
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