Dynamics of the Bianchi~V cosmological model inspired by quintessential $\alpha$-attractors

Abstract

We investigate scalar-field cosmologies in the Bianchi V spacetime using a dynamical-systems framework. Motivated by representative $\alpha$-attractor potentials - the E-model and T-model - we apply averaging theorems and amplitude--phase reductions to monomial potentials $\sim {\varphi }^{2n}$ of the scalar field, which approximate the attractor models near their minima, in the presence of matter with barotropic index $\gamma$. The reduced averaged system admits five generic isolated equilibria: Kasner vacua ${\mathcal{K}}_0^{\pm }$, the matter FLRW point $\mathcal{F}$, the scalar FLRW point $\mathcal{S}$, and the curvature Milne-type point $\mathcal{K}$, together with special families for tuned $(n,\gamma )$. We find that ${\mathcal{K}}_0^{\pm }$ are always sources, $\mathcal{F}$ is generically a saddle but can act as a sink for $\gamma <\min \{\frac{2n}{n+1},\frac{2}{3}\}$, $\mathcal{S}$ is a sink if $0<n<\frac{1}{2}$ and $\frac{2n}{n+1}<\gamma \le 2$, while $\mathcal{K}$ becomes a sink whenever $\gamma >\frac{2}{3}$ and $n>\frac{1}{2}$. These results demonstrate that isotropic FLRW $\alpha$-attractor models extend naturally to anisotropic Bianchi~V cosmologies: inflationary attractors remain robust, while the Milne-type curvature solution emerges as the late-time state.

32 pages, 8 compound figures, 3 tables