Statistical Anisotropy from Anisotropic Inflation

TL;DR

The paper demonstrates that anisotropic inflation can arise naturally in supergravity via a vector field coupled to the inflaton, yielding a controlled, persistent but small anisotropy in expansion. It develops a perturbative framework, shows a universal relation $\frac{\Sigma}{H} = \frac{1}{3} I \epsilon_H$, and proves anisotropic inflation is an attractor across broad model classes. It predicts statistical anisotropy in scalar and tensor fluctuations, with calculable amplitudes $g_s$, $g_t$, and cross-correlations that obey consistency relations testable by CMB observations. The work also outlines observational strategies to detect or bound these effects (off-diagonal CMB spectra, cross-correlations) and discusses constraints on gauge kinetic functions, highlighting the potential to falsify or confirm anisotropic inflation as a competing paradigm to isotropic slow-roll inflation.

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).

Figures (5)

• Figure 1: The phase flow in $X$-$Y$-$Z$ space is shown for $\lambda = 0.1, \rho=50$. The trajectories converge to the anisotropic fixed point.
• Figure 2: Phase flow for $\phi$ is shown. Here, we took the parameters $c=2$ and $\kappa m=10^{-5}$. We also took initial conditions $\phi_i=12$ and $\dot{\phi}_i=0$. There are two different slow-roll phases. The transition occurs around $\kappa\phi= 9$.
• Figure 3: Evolutions of the anisotropy $\Sigma/H$ for various $c$ with respect to the $e$-folding number are shown. One can see the attractor behavior of the anisotropy.
• Figure 4: The TT spectra $C^{TT}_{\ell , \ell +2}$ induced by anisotropy in scalar perturbations, that in tensor perturbations and cross correlation. The parameters are chosen as $g_s =0.3,\ r=0.3$.
• Figure 5: The TB and EB spectra $C^{TB}_{\ell , \ell +1}$, $C^{EB}_{\ell , \ell +1}$ induced by the cross correlation. As a reference, the conventional diagonal BB spectrum induced by isotropic part of the tensor perturbations is plotted with a dotted line. The parameters are taken as $g_s =0.3,\ r=0.3$.