Stability of hyperbolic and matter-dominated bounce cosmologies from F(R, G) modified gravity at late evolution stages

The stability of two different bounce scenarios from F(R,G) modified gravity at later times is studied, namely a hyperbolic cosine bounce model and a matter-dominated one. After describing the main characteristics of F(R,G) modified gravity, the two different bounce scenarios stemming from this theory are reconstructed and their stability at late stages is discussed. The stability of the hyperbolic cosine model is proven, while the concrete matter-bounce model here chosen does not seem to accomplish the necessary conditions to be stable at later times.