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Дата последнего поиска статьи во внешних источниках: 16 апреля 2014 г.
Аннотация:
We study cosmological solutions in R + βRN-gravity for an isotropic Universe filled with ordinary matter with the equation of state parameter γ. Using the Bogolyubov–Krylov–Mitropol'skii averaging method we find asymptotic oscillatory solutions in terms of new functions, which have been specially introduced by us for this problem and appeared as a natural generalization of the usual sine and cosine. It is shown that the late-time behaviour of the Universe in the model under investigation is determined by the sign of the difference γ − γcrit where γcrit = 2N/(3N − 2). If γ < γcrit, the Universe reaches the regime of small oscillations near values of Hubble parameter and matter density, corresponding to general relativity solution. Otherwise higher-curvature corrections become important at late times. We also study numerically basins of attraction for the oscillatory and phantom solutions, which are present in the theory for N > 2. Some important differences between N = 2 and N > 2 cases are discussed.