Instability of anisotropic cosmological solutions supported by vector fields

Abstract: Models with vector fields acquiring a non-vanishing vacuum expectation value along one spatial direction have been proposed to sustain a prolonged stage of anisotropic accelerated expansion. Such models have been used for realizations of early time inflation, with a possible relation to the large scale CMB anomalies, or of the late time dark energy. We show that, quite generally, the concrete realizations proposed so far are plagued by instabilities (either ghosts, or unstable growth of the linearized perturbations) which can be ultimately related to the longitudinal vector polarization present in them. Phenomenological results based on these models are therefore unreliable.

• The paper identifies ghost instabilities in vector field-driven anisotropic models, undermining their potential for modeling inflation and late-time acceleration.
• It employs perturbation analysis on Bianchi-I backgrounds to reveal that the longitudinal modes exhibit uncontrolled growth at horizon crossing.
• The study underscores the need for rigorous stability checks in cosmological model-building, prompting a search for more reliable anisotropy-inducing mechanisms.

Instability of Anisotropic Cosmological Solutions Supported by Vector Fields

The paper investigates the stability of cosmological models incorporating vector fields with non-zero vacuum expectation values (vevs) aligned along a specific spatial direction, which were proposed to enable prolonged anisotropic expansion phases. This idea has been explored within contexts like early inflationary epochs and dark energy during late-time acceleration. The key takeaway from this study is the identification of fundamental instabilities—ghosts or unstable perturbation growth—associated with these models. These instabilities are intrinsically linked to the longitudinal polarization feature of the vector fields.

In detail, the paper discusses anisotropic but spatially homogeneous cosmological models classified under Bianchi models, with particular attention given to the simplest Bianchi-I backgrounds. Observational data from the WMAP experiment have motivated these studies by revealing apparent anomalies, such as the low quadrupole moment power and multipole alignment, termed the 'axis-of-evil.' These phenomena hint at possible deviations from isotropy in the early Universe, which isotropic inflation models fail to sufficiently explain.

The authors analyze the theoretical foundations of employing vector fields with non-zero spatial vevs as sources of anisotropy. This approach has been realized through different model classes, all of which this paper scrutinizes for stability:

1. The original model from 1989, involving a potential term only affecting the vector field,
2. A recent formulation with non-minimal coupling to curvature,
3. Models using a Lagrange multiplier to maintain a space-like vev.

These models were subjected to perturbation analysis to assess linear stability. The study reveals that irrespective of the realization, each model exhibits instability related to the longitudinal vector mode, primarily characterized by ghost-like behavior or uncontrolled perturbation growth upon horizon crossing.

Furthermore, practical implications from models leveraging such anisotropy-inducing mechanisms are rendered unreliable due to the identified instabilities. The paper suggests that even minor anisotropic effects may build up, leading to substantial deviations in cosmic microwave background (CMB) patterns, should these models be practically viable.

The meticulous examination highlights the instabilities prevalent at small or large wavelengths, typically arising at horizon crossings, where perturbations transition from inside to outside the Hubble horizon. In some realizations, the perturbations within standard kinetic terms reveal tachyonic behavior.

Nevertheless, the analysis emphasizes the constraints of the models explored and raises a cautionary note that not all conceivable vector-field-based scenarios might be destabilized. The research primarily questions the reliability of standard vector field models in providing a stable and predictable basis for anisotropic inflationary or acceleration scenarios within cosmological settings.

The study concludes with implications for future developments in the field of cosmological model-building and perturbation analysis. It calls for rigorous stability checks for any proposed model employing vector fields as mechanisms for anisotropic expansion. Even though the paper demonstrates substantial issues within current models, it invites possible constructive adaptations and potential breakthroughs in overcoming the fundamental challenges discovered.

This paper’s findings impose a crucial reevaluation of methods by which anisotropies are introduced in cosmological models, urging developments that can address and possibly rectify the identified instabilities while remaining consistent with observational data. Such advancements would significantly contribute to the theoretical constructs surrounding early universe conditions and dark energy interpretations.