Bianchi type I anisotropic power-law solutions for the Galileon models

Abstract

We will study the cosmological solutions of a class of Galileon models. A special class of the Bianchi type I power-law solutions will be presented in this paper. We will show that these Bianchi type I power-law solutions are stable during the inflationary phase. In addition, we will also show that the presence of a phantom field induces at least an unstable mode for the perturbation equation and destabilizes the powerlaw solutions.

Anisotropic power-law inflation for a conformal-violating Maxwell model

“…On the other hand, Eq. (4.6) admits at least one positive root if a 1 a 6 < 0 [47][48][49][50][51][52]. Therefore the corresponding anisotropic solution is unstable if a 1 a 6 < 0.…”

“…In particular, we would like to obtain a new set of power-law analytic solutions with the form [43,44,[47][48][49][50][51][52]:…”

“…In order to understand the stability of the set of power-law solutions, we will consider the power-law perturbation of the field equations with δα = A α t m , δσ = A σ t m , and δφ = A φ t m [47][48][49][50][51][52]. Perturbing Eqs.…”

“…In particular, the anisotropy will survive the inflation if I is chosen to be a canonical function of a scalar field as shown in the KSW model [43,44,[49][50][51][52]. On the other hand, if I is chosen as a function of the kinetic term of the scalar field, the anisotropy is unstable during the inflationary phase.…”

“…More interestingly, non-canonical extensions of the KSW model, in which a scalar field takes non-canonical form such as Dirac-Born-Infeld (DBI), supersymmetric Dirac-BornInfeld (SDBI), and covariant Galileon forms, have also been shown to admit stable and attractive Bianchi type I inflationary solutions [49][50][51][52]. This indicates that the cosmic no-hair conjecture does not hold for the extended KSW models due to the presence of the coupling term f 2 (φ)F μν F μν .…”