Inflationary α -attractor cosmology: A global dynamical systems perspective

Abstract

This is the published version of a paper published in Physical Review D: covering particles, fields, gravitation, and cosmology.Citation for the original published paper (version of record):Alho, A., Uggla, C. (2017) Inflationary alpha-attractor cosmology: A global dynamical systems perspective. We study flat Friedmann-Lemaître-Robertson-Walker α-attractor E-and T-models by introducing a dynamical systems framework that yields regularized unconstrained field equations on two-dimensional compact state spaces. This results in both illustrative figures and a complete description of the entire solution spaces of these models, including asymptotics. In particular, it is shown that observational viability, which requires a sufficient number of e-folds, is associated with a particular solution given by a one-dimensional center manifold of a past asymptotic de Sitter state, where the center manifold structure also explains why nearby solutions are attracted to this "inflationary attractor solution." A center manifold expansion yields a description of the inflationary regime with arbitrary analytic accuracy, where the slowroll approximation asymptotically describes the tangency condition of the center manifold at the asymptotic de Sitter state. Physical

Extended phase-space analysis of the Hořava–Lifshitz cosmology

“…[104] has f (s) = − s 2 2n . The so-called E-model studied from the dynamical systems point of view in [105] has potential V (φ) [120][121][122] has f (s) = −(s + α)(s + β).…”

“…discussed previously in [104] for a conventional scalar field while in Sect. 3.4 it is studied the E-model with potential V (φ) = V 0 1 − e − 2 3α φ 2n discussed in [105] for a conventional scalar field cosmology. The methodology we use is different from that employed in [104,105], and we apply the potentials in a different context.…”

“…3.4 it is studied the E-model with potential V (φ) = V 0 1 − e − 2 3α φ 2n discussed in [105] for a conventional scalar field cosmology. The methodology we use is different from that employed in [104,105], and we apply the potentials in a different context. However, we complimentary use analogous variables as in [104,105] to make comparisons with the relativistic case.…”

“…The methodology we use is different from that employed in [104,105], and we apply the potentials in a different context. However, we complimentary use analogous variables as in [104,105] to make comparisons with the relativistic case. The analogous analysis is done in Sect.…”

T -model inflation and bouncing cosmology

“…V (φ) = Λ tanh 2 ( φ √ 6α ). A complete analysis of these models in the context of dynamical systems was recently completed [23], in which the extended behaviour of the entire system was found to have unique endpoints under evolution, and the universality of such evolutions was established.…”