Cosmology with nonminimal kinetic coupling and a power-law potential

Understand

We consider cosmological dynamics in the theory of gravity with the scalar field possessing a nonminimal kinetic coupling to gravity, $\kappa G_{\mu\nu}\phi^{\mu}\phi^{\nu}$, and the power-law potential $V(\phi)=V_0\phi^N$.

• 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 $H={1}/{\sqrt{9\kappa}}$ 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 $\kappa$.
• We obtain that there exist two different late-time asymptotical regimes.