Cosmology with nonminimal kinetic coupling and a Higgs-like potential

TL;DR

This paper explores cosmological models with a scalar Higgs-like field coupled nonminimally to gravity, revealing scenarios like late-time inflation, Big Rip, and Little Rip through dynamical system analysis.

Contribution

It introduces a novel analysis of Higgs-like scalar fields with nonminimal kinetic coupling, identifying new accelerated expansion regimes and deriving modified slow-roll conditions.

Findings

Existence of late-time inflation with constant Hubble parameter.

Identification of Big Rip and Little Rip cosmological scenarios.

Modified slow-roll conditions leading to Little Rip.

Abstract

We consider cosmological dynamics in the theory of gravity with the scalar field possessing the nonminimal kinetic coupling to curvature given as $\kappa G^{\mu\nu}\phi_{,\mu}\phi_{,\nu}$, and the Higgs-like potential $V(\phi)=\frac{\lambda}{4}(\phi^2-\phi_0^2)^2$. Using the dynamical system method, we analyze stationary points, 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) {\em The late-time inflation} when the Hubble parameter tends to the constant value, $H(t)\to H_\infty=(\frac23 \pi G\lambda\phi_0^4)^{1/2}$ as $t\to\infty$, while the scalar field tends to zero, $\phi(t)\to 0$, so that the Higgs potential reaches its local maximum $V(0)=\frac14 \lambda\phi_0^4$. (ii) {\em The Big Rip} when $H(t)\sim(t_*-t)^{-1}\to\infty$ and $\phi(t)\sim(t_*-t)^{-2}\to\infty$ as $t\to t_*$. (iii) {\em The Little Rip} when $H(t)\sim t^{1/2}\to\infty$ and $\phi(t)\sim t^{1/4}\to\infty$ as $t\to\infty$. Also, we derive modified slow-roll conditions for the Higgs field and demonstrate that they lead to the Little Rip scenario.