Primordial black holes with anisotropic hair

TL;DR

The paper investigates how anisotropic inflation driven by a vector field with a kinetic coupling $f^2(\phi)F_{\mu\nu}F^{\mu\nu}$ can generate large, anisotropic curvature perturbations on small scales that seed primordial black holes (PBHs). In the strong-mixing regime $\mathcal{I} \gg 1$, integrating out the heavy scalar perturbation yields an effective theory for the vector perturbation with an angle-dependent sound speed $c_s^2(\theta)=\cos 2\theta$, which becomes negative in certain angular ranges, causing exponential growth of perturbations. The resulting curvature power spectrum exhibits an exponential, highly anisotropic enhancement $\Delta_{\mathcal{R}} \sim e^{4\pi\left|\sin\theta-\tfrac{\sqrt{2}}{2}\right|\mathcal{I}}$ around a small-scale peak at $k_p(\theta)$, with maximal amplification near $\theta=\tfrac{\pi}{2}$. The authors illustrate the mechanism with a toy two-field model and discuss observational implications, including PBH abundance, scalar-induced gravitational waves, and potential tests of the cosmic no-hair conjecture beginning with anisotropic signatures in the stochastic backgrounds.

Abstract

A mechanism for generating anisotropic enhancements of the curvature perturbation through a vector field is proposed. We find that when the mixing between the inflaton perturbation and the vector-field perturbation is sufficiently strong in the anisotropic inflation, the power spectrum becomes dominated by anisotropic constant modes. This suggests that statistical anisotropy in primordial black hole (PBH) formation may be inevitable if inflation undergoes an anisotropic inflationary phase. Our findings offer a novel approach to probe vector fields during inflation and to test the cosmic no-hair conjecture.

Figures (1)

• Figure 1: The power spectrum of $\mathcal{R}$ for our toy example (\ref{['toyP']}). We use the Gaussian profile $\mathcal{I}(N)=\mathcal{I}_{\text{max}} e^{-(N-N_f)^2/(2\Delta N^2)}$ with $\mathcal{I}_{\text{max}}=5$, $\Delta N=2$, $N_f\simeq N_{\text{CMB}}+5$ and $r_{\text{ini}}=10$. $\mathcal{P}_{\mathcal{A}}=\mathcal{P}_0\left|2-4\sin^2\theta\right|^{1/2}e^{4\pi\left|\sin{\theta}-\frac{\sqrt{2}}{2}\right|\mathcal{I}}{|}_{N_v(k)}$, where $N_v(k)$ is given by $p(N_v)=|m_{\varphi}(N_v)|$. The black curve represent peaks $k_p(\theta)$ of $\mathcal{P}_{\mathcal{R}}$.