Evgeny E. Bukzhalev, Mikhail M. Ivanov, Alexey V. Toporensky
We study cosmological solutions in $R + \beta R^{N}$-gravity for an isotropic Universe filled with an ordinary matter with the equation of state parameter $\gamma$. Using Bogolyubov-Krylov-Mitropol'skii averaging method we find asymptotic solutions in terms of new functions, specially introduced by us for this problem. It is shown that the late-time behaviour of the Universe in the model under investigation is determined by the sign of the difference $\gamma-\gamma_{crit}$ where $\gamma_{crit}=2N/(3N-2)$. If $\gamma < \gamma_{crit}$, the Universe reaches the regime of small oscillations near values of Hubble parameter and matter density, corresponding to GR 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.
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http://arxiv.org/abs/1306.5971
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