[论文解读] Cosmological angular momentum from quantum rotation

Bo-Qiang Lu|arXiv (Cornell University)|Mar 16, 2026

Cosmology and Gravitation Theories被引用 0

一句话总结

该论文提出一种机制，在通胀期间将旁观者 U(1) 标量场的内部角动量转化为空间角动量，可能在非球对称塌缩中使原始黑洞获得高自旋，与小尺度功率谱相关联。

ABSTRACT

The origin of cosmic angular momentum is a fundamental question in structure formation. We propose a novel mechanism that generates spatial angular momentum directly from quantum fluctuations during inflation. A spectator complex scalar field with global U(1) symmetry stores internal angular momentum via field-space rotation. Inflationary perturbations create spatial gradients that, upon horizon re-entry, couple to the background charge density and source a bulk momentum flow. During nonspherical gravitational collapse, this flow converts into net angular momentum. For primordial black holes forming from such collapse, the dimensionless spin can reach \(χ\sim 0.1-1\) when the small-scale power spectrum is enhanced to produce detectable abundances-far exceeding tidal torque theory predictions. This establishes a testable link between inflation, primordial perturbations, and black hole spin distributions accessible to gravitational-wave observations.

研究动机与目标

• Motivate the origin of cosmic angular momentum beyond tidal torque theory (TTT).
• Propose a fundamental mechanism where quantum fluctuations during inflation generate internal angular momentum that becomes spatial angular momentum.
• Connect PBH spin to the small-scale power spectrum and inflationary perturbations.
• Explore observational consequences for gravitational-wave astronomy and PBH phenomenology.

提出的方法

• Introduce a spectator complex scalar field with global U(1) symmetry and a radial/phase decomposition P = (S/√2) e^{iθ}.
• Identify the conserved U(1) charge density n_c = S^2 dot{θ} and analyze how inflationary perturbations seed spatial gradients δS and δθ.
• Derive the linearized momentum density T_{0i} and show dominance of S_0^2 dot{θ}_0 ∂_i δθ due to large background charge.
• Compute the total angular momentum J_{ij} from T_{0i} and show it reduces to a surface integral for spherical collapse; demonstrate it vanishes for spherical collapse but can be nonzero for ellipsoidal (quadrupolar) collapse.
• Relate perturbation spectra Δ_{δS}^2 and Δ_{δθ}^2 to the inflationary H_inf and discuss scale-invariance (n_s ≈ 1).
• Estimate the PBH spin χ in terms of the small-scale power spectrum and discuss conditions for achieving χ ~ 0.1–1.

实验结果

研究问题

• RQ1 Can internal angular momentum stored in a U(1) charged scalar field during inflation be converted into spatial angular momentum during horizon re-entry?
• RQ2 Under what collapse geometries (spherical vs ellipsoidal) does this mechanism generate net angular momentum for PBHs?
• RQ3 How does the small-scale power spectrum influence the resulting PBH spin distribution in this framework?
• RQ4 What observational signatures in gravitational waves or PBH abundances would distinguish this mechanism from tidal torque theory?
• RQ5 How large must the small-scale power be to yield detectable PBH spins without violating cosmological constraints?

主要发现

• A dominant T_{0i} contribution arises from the phase perturbation, amplified by the background U(1) charge density, enabling conversion of internal rotation to bulk momentum.
• For spherical collapse, the angular momentum J_i vanishes identically regardless of δθ(Ω).
• Ellipsoidal (quadrupolar) collapse yields nonzero angular momentum, with J_i dependent on the quadrupole perturbation Q_{ab} and the second-moment tensor of the volume.
• The PBH spin χ is linked to the inflationary perturbation amplitude Δ_{δS} via χ ~ ε (Δ_{δS}/M_Pl) or χ ~ (H_inf/M_Pl) up to order-one factors, implying negligible spin for scale-invariant spectra but potential enhancement with a boosted small-scale power spectrum.
• For detectable PBH abundances via LVK-era observations, a boosted small-scale power spectrum can yield χ in the range ~0.1–1, significantly larger than tidal torque predictions.
• The mechanism provides a testable link between inflationary quantum fluctuations, small-scale perturbations, and PBH spin distributions accessible to gravitational-wave observations.