Аннотация
This paper considers models arising from the composition of the modified Gauss–Bonnet gravity (the Gauss–Bonnet invariant) and the general relativity (the Ricci scalar) against the background of a flat, homogeneous, and isotropic space-time described by the Friedmann–Robertson–Walker metric. Advantages arising fromapplying a theory containing higher-order invariants (Gauss–Bonnet invariant) consist in the presence of additional degrees of freedom, which makes it possible to study the influence of small-order effects on the dynamics of the system under study, which are in search and confirmed by cosmological observational data. We reconstructed two models with a power-law and exponential dependence on the Gauss–Bonnet invariant, where the model ansatz is a combination of the inverse Weierstrass elliptic function and the power-law function describing the Hubble parameter. This facilitates obtaining a quasi-Dieter law of the change of the scale factor in the initial and late epochs of the Universe. The application of the special function is inspired by generalization equation of state of the Chaplygin gas type, the Weierstrass gas. The application of the equation of state with such dependence makes allows obtaining a quasi-periodic universe. The equations of state are based on the Chaplygin gas are model equations of state and describe well the evolution of both the early and the modern universe. The obtained two particular models are investigated for the fulfillment of the energy conditions, which makes it possible to carry out analysis at a late stage of evolution of the universe and using perturbation theory covering the period of the early universe. For the power-law and exponential models, the perturbations of the Hubble parameter decrease in a finite time are shown, providing a way out of the inflationary stage of evolution of the universe.