How attractive is the isotropic attractor solution of axion-SU(2) inflation?

Abstract

The key to the phenomenological success of inflation models with axion and SU(2) gauge fields is the isotropic background of the SU(2) field. Previous studies showed that this isotropic background is an attractor solution during inflation starting from anisotropic (Bianchi type I) spacetime; however, not all possible initial anisotropic parameter space was explored. In this paper, we explore more generic initial conditions without assuming the initial slow-roll dynamics. We find some initial anisotropic parameter space which does not lead to the isotropic background, but to violation of slow-roll conditions, terminating inflation prematurely. The basin of attraction increases when we introduce another scalar field acting as inflaton and make the axion-SU(2) system a spectator sector. Therefore, the spectator axion-SU(2) model is phenomenologically more attractive.

The isotropic attractor solution of axion-SU(2) inflation: Universal isotropization in Bianchi type-I geometry

“…Consequently, we see the entire phase space converges to the FLRW metric. The area previously failing to converge (the white region in the left panel) [1] coincides with the region in which β changes signs during the evolution. This plot shows the system studied in [1] with the parameters given in table 2.…”

“…The aim of this paper was to study this system with a different parametrization to investigate the nature of the no-go area in detail. We found that the numerical breakdown observed in [1] was an artifact of performing the numerical analysis based on the (ψ, β) parametrization, which is not well-defined at β = 0 and unstable at β → ±∞. This is problematic in the no-go area, i.e., large gauge field's kinetic term, in which the β(t) field switches sign during its evolution.…”

“…In [1], a similar setup but with different parameters (reproduced in table 2; small gauge coupling, g A = 2×10 −6 and λ as large as 2000) has been studied in terms of (ψ, β) parametrization for the VEV. It was shown that a sizable part of the parameter space was unstable, the Figure 3.…”

“…In this section we compare the geometry of the SU(2) gauge field's VEV in terms of (ψ, β) and (ψ 1 , ψ 2 ) parametrizations. This system was numerically studied recently using the (ψ, β) parametrization [1]. It showed that in part of the anisotropic phase space with large values of β0 /(H 0 β 0 ), the equations of motion failed due to a runaway effect of a kinetic term in the gauge fields energy density.…”

Unavoidable shear from quantum fluctuations in contracting cosmologies

“…In Ref. [26], the classical isotropisation of inflating space times in the presence of SU(2)-gauge fields coupled with an axion was also studied, and it was shown that some initial configurations lead to a premature termination of slow-roll inflation if the axion drives inflation. In Ref.…”