Some Models of Cyclic and Knot Universes
  In this paper, we obtained a class of oscillatory, cyclic and knot type solutions from the non-linear Friedmann equations. This is performed by choosing specific forms of energy density and pressure of matter. All the expressions written here are in dimensionless form. We show that evolutionary path taken by the spatial coordinates in the model follow various knots, specifically trefoil and eight-knots. We provide several examples and plot relevant cosmological parameters in figures. Our cyclic models can be interpreted as a periodic cosmological model, such that early and late time acceleration are unified under the same mechanism. 
K.R. Yesmakhanova, N. A. Myrzakulov, K. K. Yerzhanov, G.N. Nugmanova,   N.S. Serikbayaev and R. Myrzakulov
physics.gen-ph