### Speaker

Prof.
S. V. Sushkov
(Institute of Physics, Kazan Federal University)

### Description

In this work we continue an investigation of cosmological scenarios in the theory of gravity
with the scalar field possessing a non-minimal kinetic coupling to the curvature, $\kappa\, G_{\mu\nu}\phi^{\mu}\phi^{\nu}$,
[1-4]. Earlier, it was 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
$H_\kappa = 1/ \sqrt{9\kappa}$. In Ref. [4] we have studied the role of a power-law potential in models with non-minimal kinetic coupling. Now, we consider cosmological dynamics in such the models with the Higgs-like potential $V (\phi ) = (\lambda /4)(\phi^2 − \phi^2_0)^2$. Using the dynamical system method, we analyze all possible asymptotical regimes of the model under investigation. As the most important result, we have found that, if the nonminimal coupling parameter κ is large enough to satisfy $2\pi G\kappa \lambda \phi^4_0 > 1$, then the local maximum of the Higgs potential becomes a stable node, and in this case one gets a late-time quasi-De Sitter evolution of the Universe. The cosmological constant in this epoch is $\Lambda_\infty =
3H_\infty^2 = 2\pi\lambda\phi_0^4$, and the Higgs potential reaches its local maximum $V (0) = \lambda\phi^4_0/4$. Additionally, using a numerical analysis, we construct exact solutions and find initial conditions leading to various cosmological scenarios.

### Primary author

Prof.
S. V. Sushkov
(Institute of Physics, Kazan Federal University)