Dynamical analysis of anisotropic inflation

Abstract

The inflaton coupling to a vector field via the f (ϕ) 2 Fµν F µν term is used in several contexts in the literature, such as to generate primordial magnetic fields, to produce statistically anisotropic curvature perturbation, to support anisotropic inflation, and to circumvent the η-problem. In this work, I perform dynamical analysis of this system allowing for the most general Bianchi I initial conditions. I also confirm the stability of attractor fixed points along phase-space directions that had not been investigated before. Mod. Phys. Lett. A Downloaded from www.worldscientific.com by PURDUE UNIVERSITY on 06/27/16. For personal use only. M. KarčiauskasGenerally, vector field contribution to the curvature perturbation introduces quadrupolar angular dependence of the power spectrum. In Ref. 12 (see also it was shown that observational constraints on such modulation put very stringent bounds on vector field models. This bound, however, was applied for a particular model of Ref. 16. As it is shown in later sections, a much larger parameter space might be available for model building.In this work, I perform a classical dynamical analysis of the system with a scalar and a vector field which interacts via a f 2 (ϕ)F µν F µν coupling. A similar analysis has been performed in Ref. 17 and much more generally in Ref. 10. It has been also applied in many other contexts, for example, a system of non-Abelian vector fields, 18 a vector field plus a two-form field 19 or DBI type action. 20 Building on the former two works, especially Ref. 10, I extend their treatment by including more general initial conditions and by addressing several issues which have been overlooked in previous works. I also provide exact analytic expressions to determine the asymptotic behavior of this dynamical system.A vector field introduces anisotropic stress. If it contributes to the expansion of the universe, the expansion will be anisotropic. As the (homogeneous, spacelike) vector field picks out only one preferred direction in space, we can assume that the anisotropy of the expansion will be of the axisymmetric Bianchi type I. Moreover, the preferred axis of such anisotropy will be aligned with the direction of the vector field. These two constraints were imposed in previous works on a single vector field. Even if such a configuration is self-consistent, initial conditions can be much more general. In this work, I relax both the constraints and confirm that the axial symmetry as well as the alignment are achieved dynamically if the vector field does not decay.In cases where the vector field is absent, a number of no-hair theorems have been proven, which state that the future attractor of any spatially homogeneous but anisotropic universe (with possible exception of Bianchi IX a ) is the isotropic Friedmann-Robertson-Walker (FRW) universe if the energy density is dominated by the potential energy of a scalar field. 22,b See Ref. 23 for a recent review and Ref. 24 for the most recent work on no-hair theorems. The presence of a vector field introd...

Anisotropic power-law inflation for a model of two scalar and two vector fields

“…It turns out that many counterexamples to the cosmic no-hair conjecture have been found not only in these extensions but also in other models shown in Refs. [52][53][54][55][56][57][58][59][60][61][62][63][64][65][66][67][68][69][70]. This result indicates that the unusual coupling f 2 (φ)F μν F μν does play an interesting role in the validity of the cosmic no-hair conjecture.…”

Narrowing the window of inflationary magnetogenesis

“…The second condition is that in order for the calculation in a fixed inflationary background to be consistent, the energy density in the electric and magnetic fields has to be negligible during inflation [5][6][7]. Significant electromagnetic contribution does not necessarily spoil inflationary magnetogenesis, but its influence on inflationary dynamics has to be taken into account [8][9][10][11][12]. The third condition is that the electromagnetic perturbations must not be so large as to spoil the success of the inflationary mechanism of generating the observed scalar perturbation [13][14][15][16][17][18][19][20].…”

“…Canonically normalising the kinetic term then leads to a field-dependent modification of the electric coupling, and keeping it perturbative constrains the range of validity of any study that does not take non-perturbative QED into account [4]. The energy density of the electromagnetic field also must not be so large as to interfere with inflation and magnetogenesis [5][6][7] (though having a significant fraction of the energy density in the electromagnetic field does not necessarily prevent inflation [8][9][10][11][12]). Moreover, even if the electromagnetic field is subdominant for the background, it is important to check that its perturbations do not spoil the success of the inflationary generation of a Gaussian spectrum of nearly scale-invariant adiabatic perturbations [13][14][15][16][17][18][19][20].…”

Anisotropic Spacetimes in Chiral Scalar Field Cosmology

“…Indeed, the parameter, β (t), is the anisotropic parameter while α (t) is the scale factor for the three-dimensional hypersurface. These spacetimes play an important role on the description of the very early universe and specifically during the pre-inflationary era [41][42][43][44][45][46][47][48][49].…”