Stable small spatial hairs in a power-law k-inflation model

Abstract

In this paper, we extend our investigation of the validity of the cosmic no-hair conjecture within non-canonical anisotropic inflation. As a result, we are able to figure out an exact Bianchi type I solution to a power-law k-inflation model in the presence of unusual coupling between scalar and electromagnetic fields as $$-f^2(\phi )F_{\mu \nu }F^{\mu \nu }/4$$ - f 2 ( ϕ ) F μ ν F μ ν / 4 . Furthermore, stability analysis based on the dynamical system method indicates that the obtained solution does admit stable and attractive hairs during an inflationary phase and therefore violates the cosmic no-hair conjecture. Finally, we show that the corresponding tensor-to-scalar ratio of this model turns out to be highly consistent with the observational data of the Planck 2018.

Anisotropic power-law inflation for a model of two scalar and two vector fields

“…This result is consistent with our previous investigations in Refs. [71,72,[82][83][84][85], in which we have shown that the inclusion of the phantom field with ω = −1 breaks down the stability of the anisotropic inflation. It is worth noting that the stability of the anisotropic fixed point can be numerically confirmed through its attractor behavior.…”

“…In particular, the stable or unstable fixed points will be shown to be attractive or unattractive, respectively. Therefore, we would like to examine whether this anisotropic fixed point is an attractor one or not, similar to the previous studies [51,[82][83][84][85][86]. To do this, we will numerically solve the dynamical system with different initial conditions and then plot the corresponding phase spaces of dynamical variables X , Y 1 , Y 2 , and Z .…”

“…In this section, we would like to investigate whether the obtained anisotropic power-law solution is attractive during the inflationary phase, following the previous investigations [51,72,[82][83][84][85]. In order to do this task, we will transform the field equations into the corresponding autonomous equations of dynamical system.…”

“…More interestingly, non-canonical scenarios, in which a non-canonical scalar field is coupled to a vector field, have been investigated in Refs. [81][82][83][84][85]. Additionally, a higher dimensional version of the KSW model has been examined in Ref.…”

Anisotropic constant-roll inflation for the Dirac–Born–Infeld model

“…Among non-trivial extensions of the KSW model, there are two interesting approaches, which we are currently interested in. The first approach is non-canonical extensions [76][77][78][79][80], in which a canonical scalar field is replaced by noncanonical ones such as the Dirac-Born-Infeld (DBI) field [76], whose origin can be realized in the D3-brane theory [98,99]. For interesting cosmological aspects of the DBI inflation, see Refs.…”