Cosmology with nonminimal kinetic coupling and a power-law potential

We consider cosmological dynamics in the theory of gravity with the scalar field possessing a nonminimal kinetic coupling to gravity, κG μνφμφν, and the power-law potential V(φ)=V0φN. Using the dynamical system method, we analyze all possible asymptotical regimes of the model under investigation and show that for sloping potentials with 0<N<2 there exists a quasi-de Sitter asymptotic H=1/√9κ corresponding to an early inflationary Universe. In contrast to the standard inflationary scenario, the kinetic coupling inflation does not depend on a scalar field potential and is only determined by the coupling parameter κ. We obtain that there exist two different late-time asymptotical regimes. The first one leads to the usual powerlike cosmological evolution with H=1/3t, while the second one represents the late-time inflationary Universe with H=1/√3κ. This secondary inflationary phase depends only on κ and is a specific feature of the model with nonminimal kinetic coupling. Additionally, an asymptotical analysis shows that for the quadric potential with N=2, the asymptotical regimes remain qualitatively the same, while the kinetic coupling inflation is impossible for steep potentials with N>2. Using a numerical analysis, we also construct exact cosmological solutions and find initial conditions leading to the initial kinetic coupling inflation followed either by a "graceful" oscillatory exit or by the secondary inflation. © 2013 American Physical Society.