Statistical Anisotropy from Anisotropic Inflation (1201.6434v2)

Abstract: We review an inflationary scenario with the anisotropic expansion rate. An anisotropic inflationary universe can be realized by a vector field coupled with an inflaton, which can be regarded as a counter example to the cosmic no-hair conjecture. We show generality of anisotropic inflation and derive a universal property. We formulate cosmological perturbation theory in anisotropic inflation. Using the formalism, we show anisotropic inflation gives rise to the statistical anisotropy in primordial fluctuations. We also explain a method to test anisotropic inflation using the cosmic microwave background radiation (CMB).

• The paper introduces a vector field-coupled inflation model that challenges the cosmic no-hair conjecture.
• It derives a quantitative relation, Σ/H = (1/3)Iε_H, linking anisotropy to slow-roll parameters, with clear implications for CMB observations.
• The work predicts measurable cross-correlations between scalar and tensor perturbations, offering actionable tests through gravitational wave signatures.

Anisotropic Inflation: Implications for Cosmological Models and Observations

The paper "Statistical Anisotropy from Anisotropic Inflation" by Jiro Soda explores a critical deviation from the cosmic no-hair conjecture, offering a compelling framework for understanding anisotropic inflation driven by vector fields. This approach provides a unique theoretical basis for the statistical anisotropy observed in primordial fluctuations, with potential testability through cosmic microwave background radiation (CMB) data.

Key Findings and Theoretical Constructs

Soda's work investigates an inflationary scenario where a vector field is coupled to an inflaton, resulting in anisotropic expansion rates. The introduction of vector fields offers a counterexample to the cosmic no-hair conjecture, which posits the isotropization of the universe through inflation. This paper methodically formulates cosmological perturbation theory in the context of anisotropic inflation, demonstrating how these vector fields can result in statistical anisotropy in primordial fluctuations.

The derivations in the paper lead to several quantitative relationships, most notably the universal property of anisotropic inflation characterized by the anisotropy degree $\Sigma/H = \frac{1}{3}I\epsilon_H$, where $\epsilon_H$ quantifies the deviation from De Sitter space and $I$ captures model-specific parameters. This relation highlights that the degree of anisotropy is inherently limited to the order of the slow-roll parameter $\epsilon_H$.

Observational Implications and Predictions

The paper suggests several observational consequences of anisotropic inflation. Primarily, the statistical anisotropy of curvature perturbations can be expressed as $g_s = 24IN^2(k)$, where $N(k)$ is the $e$-folding number from the horizon exit to the end of inflation. This anisotropy can also manifest in the tensor perturbations, leading to observable effects in gravitational waves, quantified by $g_t = 6I\epsilon_HN^2(k)$.

The paper further predicts cross-correlations between curvature perturbations and gravitational waves given by $r_c = -24\sqrt{2}I\epsilon_HN^2(k)$. These predictions are encapsulated in consistency relations that offer a model-independent mechanism to test the validity of anisotropic inflation theories.

Testing Anisotropic Inflation Through CMB Observations

Soda's framework indicates that precision measurements of the CMB could potentially reveal statistical anisotropies, providing a pathway to test these theoretical models. For instance, anisotropies in scalar perturbations are constrained by current observations to $g_s < 0.3$, with aspirations for deeper scrutiny through future CMB data. The consistency relations derived in the paper can further assist in distinguishing anisotropic inflationary predictions from other cosmological models.

Future Directions and Speculations

The research opens avenues for exploring a wider range of anisotropic inflationary models, such as those incorporating different kinetic terms or additional gauge fields. The implications of anisotropic inflation for primordial magnetic fields and the generation of large-scale structure anomalies warrant further investigation.

Additionally, discerning the sub-dominant scale of anisotropy necessitates advanced observational techniques to differentiate these effects from isotropic major influences. Tools such as next-generation satellite missions or ground-based telescopes with enhanced sensitivity to the polarization of CMB might offer such capabilities.

Conclusion

Soda's exploration into anisotropic inflation serves as a significant contribution to understanding potential deviations from homogeneity and isotropy in the early universe. By providing both a theoretical basis and observational prospects, this research deepens our grasp of inflationary dynamics and enhances the dialogue between theoretical models and observational cosmology. As precision cosmology evolves, these insights have the potential to refine our understanding of the inflationary paradigm and its role in shaping cosmic anisotropies.