Cosmology with nonminimal kinetic coupling and a Higgs-like potential

We consider cosmological dynamics in the theory of gravity with the scalar field possessing the nonminimal kinetic coupling to curvature given as kappa G(mu nu)phi(nu), and the Higgs-like potential V(phi) = lambda/4 (phi(2)-phi(2)(0))(2) . Using the dynamical system method, we analyze stationary POI nts, their stability, and all possible asymptotical regimes of the model under consideration. We show that the Higgs field with the kinetic coupling provides an existence of accelerated regimes of the Universe evolution. There are three possible cosmological scenarios with acceleration: (i) The late-time de Sitter epoch when the Hubble paranwter tends to the constant value, H(t) -> H-infinity = (2/3 pi G lambda phi(4)(0)) as t -> infinity while the scalar field tends to zero, phi(t) -> 0, so that the Higgs potential reaches its local maximum V(0) - Av. (ii) The Big Rip when H(1) similar to (t* - 1)(-1) -> and - (1, -1)(-2) DO as t -> infinity. (iii) The Little Rip when H(t) t112 oo and OM 0/1 > OC as t x). Also, we derive modified slow-roll conditions for the Higgs field and demonstrate that they lead to the Little Rip scenario.