Inflation with stable anisotropic hair: is it cosmologically viable?

Abstract

Recently an inflationary model with a vector field coupled to the inflaton was proposed and the phenomenology studied for the Bianchi type I spacetime. It was found that the model demonstrates a counter-example to the cosmic no-hair theorem since there exists a stable anisotropically inflationary fix-point. One of the great triumphs of inflation, however, is that it explains the observed flatness and isotropy of the universe today without requiring special initial conditions. Any acceptable model for inflation should thus explain these observations in a satisfactory way. To check whether the model meets this requirement, we introduce curvature to the background geometry and consider axisymmetric spacetimes of Bianchi type II,III and the Kantowski-Sachs metric. We show that the anisotropic Bianchi type I fix-point is an attractor for the entire family of such spacetimes. The model is predictive in the sense that the universe gets close to this fix-point after a few e-folds for a wide range of initial conditions. If inflation lasts for N e-folds, the curvature at the end of inflation is typically of order ∼ e −2N . The anisotropy in the expansion rate at the end of inflation, on the other hand, while being small on the one-percent level, is highly significant. We show that after the end of inflation there will be a period of isotropization lasting for ∼ 2 3 N e-folds. After that the shear scales as the curvature and becomes dominant around N e-folds after the end of inflation. For plausible bounds on the reheat temperature the minimum number of e-folds during inflation, required for consistency with the isotropy of the supernova Ia data, lays in the interval (21, 48). Thus the results obtained for our restricted class of spacetimes indicates that inflation with anisotropic hair is cosmologically viable.

Anisotropic inflation with general potentials

“…(7),σ is also neglected. Moreover, from Eq.s (5), (6), (9), (12) and (14) we can obtain the slow-roll parameters:…”

“…Such a viable model has been proposed in [5] (see also [6]), in which the inflaton field φ has the simplest mass squared term, whereas the coupling terms of the vector field to the inflaton has the form f 2 (φ)F µν F µν with an arbitrary function f (φ). In [5], it was determined that an attractor solution of R ≡ ρ A /ρ φ ∼ 10 −2 can be obtained for various parameter choices, where ρ A and ρ φ denote the energy density of the vector and the inflaton, respectively.…”

Inflationary dynamics with a non-Abelian gauge field

“…In fact there are several discussions about the dynamics of inflation, where supportive roles of gauge fields in realizing accelerated expansion have been observed [31][32][33][34][35][36][37][38][39][40][41][42].…”

Anisotropic power spectrum and bispectrum in thef(ϕ)F2mechanism

“…The classical equations of motion of the model admit an attractor solution, [19,38] characterized by a non-vanishing "electric" component E (0) . A 10% level anisotropy (|g * | = O (0.1)) is found for an energy | E (0) | 2 /2 which is about eight orders of magnitude smaller than the inflaton potential [35][36][37].…”