Realistic cosmological scenario with non-minimal kinetic coupling
  We investigate cosmological scenarios in the theory of gravity with the scalar field possessing a non-minimal kinetic coupling to the curvature. It is shown that the kinetic coupling provides an essentially new inflationary mechanism. Namely, at early cosmological times the domination of coupling terms in the field equations guarantees the quasi-De Sitter behavior of the scale factor: $a(t)\propto e^{H_{\kappa} t}$ with $H_\kappa=1/\sqrt{9\kappa}$, where $\kappa\simeq 10^{-74}$ sec$^2$ is the coupling parameter. The primary inflationary epoch driven by non-minimal kinetic coupling comes to the end at $t_f \simeq 10^{-35}$ sec. Later on, the matter terms are dominating, and the universe enters into the matter-dominated epoch which lasts approximately $0.5H_0^{-1}\sim 0.5\times10^{18}$ sec. Then, the cosmological term comes into play, and the universe enters into the secondary inflationary epoch with $a(t)\propto e^{H_{\Lambda} t}$, where $H_\Lambda=\sqrt{\Lambda/3}$. Note that the present value of the acceleration parameter $q=\ddot a a/\dot a^2$ is estimated as $q_0\simeq0.25$, that is the universe is at the beginning of the epoch of accelerated expansion. Thus, the cosmological model non-minimal kinetic coupling represents the realistic cosmological scenario which successfully describes basic cosmological epochs and provide the natural mechanism of epoch change without any fine-tuned potential. 
Sergey Sushkov
gr-qc astro-ph.CO hep-th