General dynamical properties of cosmological models with nonminimal kinetic coupling

Jiro Matsumoto; Sergey V. Sushkov

doi:10.1088/1475-7516/2018/01/040

paper

General dynamical properties of cosmological models with nonminimal kinetic coupling

arXiv:1703.04966 · doi:10.1088/1475-7516/2018/01/040

Abstract

We consider cosmological dynamics in the theory of gravity with the scalar field possessing the nonminimal kinetic coupling to curvature given as $η G^{μν} ϕ_{, μ} ϕ_{, ν}$ , where $η$ is an arbitrary coupling parameter, and the scalar potential $V (ϕ)$ which assumed to be as general as possible. With an appropriate dimensionless parametrization we represent the field equations as an autonomous dynamical system which contains ultimately only one arbitrary function $χ (x) = 8 π ∣ η ∣ V (x / 8 π)$ with $x = 8 π ϕ$ . Then, assuming the rather general properties of $χ (x)$ , we analyze stationary points and their stability, as well as all possible asymptotical regimes of the dynamical system. It has been shown that for a broad class of $χ (x)$ there exist attractors representing three accelerated regimes of the Universe evolution, including de Sitter expansion (or late-time inflation), the Little Rip scenario, and the Big Rip scenario. As the specific examples, we consider a power-law potential $V (ϕ) = M^{4} (ϕ / ϕ_{0})^{σ}$ , Higgs-like potential $V (ϕ) = \frac{λ}{4} (ϕ^{2} - ϕ_{0}^{2})^{2}$ , and exponential potential $V (ϕ) = M^{4} e^{- ϕ / ϕ_{0}}$ .

31 pages, 5 figures, 3 tables. New section "Slow-roll regime" added, references added, sentences polished. Version accepted for publication in JCAP

General dynamical properties of cosmological models with nonminimal kinetic coupling

Abstract

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