Cosmology with nonminimal kinetic coupling and a Higgs-like potential

Abstract

We consider cosmological dynamics in the theory of gravity with the scalar field possessing the nonminimal kinetic coupling to curvature given as $\kappa G^{\mu \nu }{\varphi }_{,\mu }{\varphi }_{,\nu }$, and the Higgs-like potential $V(\varphi )=\frac{\lambda }{4}({\varphi }^2-{\varphi }_0^2{)}^2$. 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, $H(t)\to H_{\infty }=(\frac{2}{3}\pi G\lambda {\varphi }_0^4{)}^{1/2}$ as $t\to \infty$, while the scalar field tends to zero, $\varphi (t)\to 0$, so that the Higgs potential reaches its local maximum $V(0)=\frac{1}{4}\lambda {\varphi }_0^4$. (ii) {\em The Big Rip} when $H(t)\sim (t_{\ast }-t{)}^{-1}\to \infty$ and $\varphi (t)\sim (t_{\ast }-t{)}^{-2}\to \infty$ as $t\to t_{\ast }$. (iii) {\em The Little Rip} when $H(t)\sim t^{1/2}\to \infty$ and $\varphi (t)\sim t^{1/4}\to \infty$ 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.

29 pages, 11 figures, discussions and references added, to be published on JCAP

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Cited by in corpus (20)

• Dynamical systems applied to cosmology: dark energy and modified gravity
• Selected topics in scalar-tensor theories and beyond
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• On the phantom barrier crossing and the bounds on the speed of sound in non-minimal derivative coupling theories
• PPN parameters in gravitational theory with nonminimally derivative coupling
• General dynamical properties of cosmological models with nonminimal kinetic coupling
• Constraints on dark energy models from the Horndeski theory
• Generalized Scalar Field Cosmologies: A Global Dynamical Systems Formulation
• Generalized scalar field cosmologies: theorems on asymptotic behavior
• Time-averaging axion-like interacting scalar fields models
• Dynamical systems analysis of the cubic galileon beyond the exponential potential and the cosmological analogue of the vDVZ discontinuity
• On viability of inflation in non-minimal kinetic coupling theory
• Thermodynamics of general scalar-tensor theory with non-minimally derivative coupling
• An issue with the classification of the scalar-tensor theories of gravity
• Curvaton reheating in non-minimal derivative coupling to gravity: NO models
• On Inflationary Models in f(R,T) Gravity with a Kinetic Coupling Term
• Symmetron with a non-minimal kinetic term
• Dynamics of holographic dark energy with apparent-horizon cutoff and non-minimal derivative coupling gravity in non-flat FLRW universe
• Exact cosmological solutions with magnetic field in the theory of gravity with non-minimal kinetic coupling
• Dynamical analysis of Brans-Dicke Universe with inverse power-law effective potential