Theory of cosmological perturbations in an anisotropic universe

Abstract

This article describes the theory of cosmological perturbations around a homogeneous and anisotropic universe of the Bianchi I type. Starting from a general parameterisation of the perturbed spacetimeà la Bardeen, a complete set of gauge invariant variables is constructed. Three physical degrees of freedom are identified and it is shown that, in the case where matter is described by a scalar field, they generalize the Mukhanov-Sasaki variables. In order to show that they are canonical variables, the action for the cosmological perturbations at second order is derived. Two major physical imprints of the primordial anisotropy are identified: (1) a scalar-tensor "see-saw" mechanism arising from the fact that scalar, vector and tensor modes do not decouple and (2) an explicit dependence of the statistical properties of the density perturbations and gravity waves on the wave-vector instead of its norm. This analysis extends, but also sheds some light on, the quantization procedure that was developed under the assumption of a Friedmann-Lemaître background spacetime, and allows to investigate the robustness of the predictions of the standard inflationary scenario with respect to the hypothesis on the symmetries of the background spacetime. These effects of a primordial anisotropy may be related to some anomalies of the cosmic microwave background anisotropies on large angular scales.

Anisotropic, nonsingular early universe model leading to a realistic cosmology

“…The model is thus reminiscent of the Taub-NUT vacuum solution in that it has biaxial Bianchi IX geometry and its evolution exhibits a dimensionality reduction at a quasi-regular singularity; the two models are, however, rather different, as we will show in a future work. Here we concentrate on the cosmological implications of our model and show how the scalar field drives both isotropisation and inflation, thus raising the question of whether structure on the largest scales was laid down at a time when the universe was still oblate (as also suggested by [1,2,3]). We also discuss the stability of our model to small perturbations around biaxiality and draw an analogy with cosmological perturbations.…”

Isotropization of the universe during inflation

“…Due to the lack of rotational invariance in BI spacetimes, the evolution of cosmological perturbations [14] differs drastically from the one found in FL universes [15]. The differences can be traced back to two main effects.…”

“…Note that the vector perturbations do not appear in the action. However, they can no longer be neglected, since they appear as constraints relating scalar and tensor modes, and it is crucial to consider them in intermediary steps when determining the form of the action [14]. When varied, this action leads to…”

Cosmic microwave background anomalies from imperfect dark energy

“…In particular it can be robustly realized by the vector curvaton paradigm (Dimopoulos et al 2010) which Dimopoulos et al (2013) has recently implemented within D-brane inflation in type II string theory by taking the U(1) gauge field into account that lives on the brane. Perturbations have also been studied in anisotropically inflating backgrounds (Pereira et al 2007;Gumrukcuoglu et al 2007) and in the shear-free cosmologies considered in and Zlosnik (2011), where the expansion is isotropic but the spatial curvature depends on the direction. These homogeneous but anisotropic universes could emerge by tunnelling from a lower dimensional vacuum (Adamek et al 2010;Graham et al 2010).…”