Extended FLRW models: dynamical cancellation of cosmological anisotropies

Abstract

We investigate a corner of the Bianchi models that has not received much attention: "extended FLRW models" (eFLRW) defined as a cosmological model with underlying anisotropic Bianchi geometry that nevertheless expands isotropically and can be mapped onto a reference FLRW model with the same expansion history. In order to investigate the stability and naturalness of such models in a dynamical systems context, we consider spatially homogeneous models that contain a massless scalar field ϕ and a non-tilted perfect fluid obeying an equation of state p = wρ. Remarkably, we find that matter anisotropies and geometrical anisotropies tend to cancel out dynamically. Hence, the expansion is asymptotically isotropic under rather general conditions. Although extended FLRW models require a special matter sector with anisotropies that are "fine-tuned" relative to geometrical anisotropies, our analysis shows that such solutions are dynamically preferred attractors in general relativity. Specifically, we prove that all locally rotationally symmetric Bianchi type III universes with space-like ∇ µ ϕ are asymptotically shear-free, for all w ∈ [−1, 1]. Moreover, all shear-free equilibrium sets with anisotropic spatial curvature are proved to be stable with respect to all homogeneous perturbations for w ≥ −1/3.1 The origin of these features is still unclear and there is an ongoing discussion if they are indicating new physics or if they are merely statistical fluctuations. See [9] for a discussion on possible implications of the tension related to the lensing amplitude, with CMB spectra favoring a positive spatial curvature at more than the 99% confidence level. For reviews on the socalled "ΛCDM anomalies", see [10][11][12] and references therein.2 In its simplest version, the cosmological principle should also postulate the Universe's spatial topology [15]. Usually, and this is the case here, this is taken to be the trivial topology.

Warm inflation with non-comoving scalar field and radiation fluid

“…The intriguing possibility that the geometry of the Universe may not be of the standard Friedmann-Lemaitre-Robertson-Walker (FLRW) form was investigated, from different points of view, in [142][143][144][145][146][147][148][149][150][151][152][153].…”

“…In particular, so-called extended FLRW models, representing a cosmological model with an underlying anisotropic Bianchi geometry that expands isotropically, and that can be mapped onto a standard FLRW model with the same expansion history, were investigated in [153]. It was found that matter and geometrical anisotropies tend to cancel out each other dynamically, and that, under rather general conditions, the expansion is asymptotically isotropic.…”

Exact Kantowski–Sachs spacetimes in Einstein–Aether scalar field theory

“…It is well-know in the GR case that for Bianchi I and Bianchi III, the Hubble parameter H is always monotonic and the anisotropy decays in time for H > 0. Therefore, isotropization occurs [20]. However, for Kantowski-Sachs, as well as for closed FLRW, the Hubble parameter is not guaranteed to be monotonic, and anisotropies would increase rather than vanish (see [21,22] and references therein).…”

“…to obtain additional information. If we exploit (19) and (20) with the means to substitute two of the momenta in expression (28), we observe that the latter leads to an algebraic relation among the configuration space variables. In particular we get…”

“…for which we assume from now on that I 2 = 0. If we turn back to the expression (20) for the integral of motion I 2 we see that, in the velocity phase space, it is written as…”