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