Abstract The dependence of chaos on two parameters of the cosmological constant and the self-interacting coefficient in the imaginary phase space for a closed Friedman-Robertson-Walker (FRW) universe with a conformally coupled scalar field, as the full understanding of the dependence in real phase space, is investigated numerically. It is found that Poincaré plots for the two parameters less than 1 are almost the same as those in the absence of the cosmological constant and self-interacting terms. For energies below the energy threshold of 0.5 for the imaginary problem in which there are no cosmological constant and self-interacting terms, an abrupt transition to chaos occurs when at least one of the two parameters is 1. However, the strength of the chaos does not increase for energies larger than the threshold. For other situations of the two parameters larger than 1, chaos is weaker, and even disappears as the two parameters increase.

Keywords cosmology: cosmological parameters—methods: numerical

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