Stability analysis of inflation with an SU(2) gauge field

Abstract

We study anisotropic cosmologies of a scalar field interacting with an SU (2) gauge field via a gauge-kinetic coupling. We analyze Bianchi class A models, which include Bianchi type I, II, VI 0 , VII 0 , VIII and IX. The linear stability of isotropic inflationary solution with background magnetic field is shown, which generalizes the known results for U (1) gauge fields. We also study anisotropic inflationary solutions, all of which turn out to be unstable. Then nonlinear stability for the isotropic inflationary solution is examined by numerically investigating the dependence of the late-time behaviour on the initial conditions. We present a number of novel features that may well affect physical predictions and viability of the models. First, in the absence of spatial curvature, strong initial anisotropy leads to a rapid oscillation of gauge field, thwarting convergence to the inflationary attractor. Secondly, the inclusion of spatial curvature destabilizes the oscillatory attractor and the global stability of the isotropic inflation with gauge field is restored. Finally, based on the numerical evidence combined with the knowledge of the eigenvalues for various inflationary solutions, we give a generic lower-bound for the duration of transient anisotropic inflation, which is inversely proportional to the slow-roll parameter. arXiv:1310.6916v2 [gr-qc] 15 Dec 2013 7 Concluding remarks 36 A Abelian dynamics 41 B Alternative numerical results tailored for Bianchi type VI 0 and VII 0 42

MHz gravitational waves from short-term anisotropic inflation

“…Since the gauge field begins to grow in the last stage of inflation, we may have a different scenario for primordial magnetic fields [42]. It is also possible to extend the present model to non-abelian cases [43][44][45] or other inflaton potentials.…”

Generalized SU(2) Proca theory

“…As already alluded to earlier, choosing SU(2) is not innocuous as we aim at cosmological applications, in view, in particular, of implementing inflation driven by gauge fields (see, e.g., Refs. [85][86][87][88][89][90][102][103][104][105][106][107][108][109][110][111][112][113][114][115]): since its adjoint representation is 3-dimensional, SU(2) permits us to generate configurations for which all three vectors are nonvanishing while ensuring isotropy.…”

Inflation driven by Barrow Holographic dark energy

“…While the late time acceleration has been attributed to the presence of dark energy (DE), the inflationary phase is assumed to be driven by a special form of DE known as the scalar fields with slow rolling assumptions [8][9][10]. Considerable amount of research has been done on inflationary models over the period of last three decades [11][12][13][14][15][16][17][18][19][20].…”