Ultralight Vector Dark Matter

• Ultralight Vector Dark Matter (UVDM) is a dark matter model featuring a coherently oscillating, extremely light vector boson (m ≲ 10⁻¹⁸ eV) with distinctive anisotropic and polarization-dependent signatures.
• Its phenomenology spans particle and wave regimes, with production mechanisms like parametric resonance and inflation-induced fluctuations, influencing structure formation and gravitational-wave propagation.
• Detection strategies leverage laboratory interferometers, quantum sensors, and pulsar timing arrays to identify UVDM's unique directional imprints and differentiate it from scalar dark matter.

Ultralight vector dark matter (UVDM) is a class of dark matter models in which the cosmological dark matter component is constituted by a coherently oscillating, extremely light vector boson with mass $m \lesssim 10^{-18}$ eV, characterized by macroscopic occupation numbers and potentially distinctive astrophysical and cosmological signatures. UVDM is motivated by both particle physics (as the gauge boson of a broken $U(1)$ symmetry, such as $U(1)_{B-L}$ or a "dark photon") and cosmology (providing alternatives to scalar "fuzzy" dark matter and standard cold dark matter). Such a field behaves as a classical, wavelike, non-relativistic spin-1 field, and its phenomenology is set by its mass, production mechanism, coupling to the Standard Model, and polarization properties. A central feature of UVDM is its capacity to imprint nontrivial anisotropic, polarization-dependent, and sometimes non-equilibrium effects on cosmic structure formation, gravitational-wave propagation, and high-precision terrestrial and astrophysical experiments.

1. Theoretical Framework and Phenomenological Regimes

Ultralight vector dark matter is typically modeled via the Proca action,

$$S = -\int d^4 x \sqrt{-g} \left[ \frac{1}{4} F^{\mu\nu} F_{\mu\nu} + \frac{1}{2} m^2 A^\mu A_\mu \right],$$

where $F_{\mu\nu} = \nabla_\mu A_\nu - \nabla_\nu A_\mu$. The key regimes governing the field's cosmological role are characterized by the ratio of comoving wavenumber $k$ to $m a$, with $a$ the scale factor (Cembranos et al., 2016):

• Particle regime ($k^2 \ll \mathcal{H} m a$): The field behaves as pressureless matter, with density perturbations indistinguishable from cold dark matter (CDM). In this limit, scalar, vector, and tensor perturbations decouple at linear order.
• Wave regime ($k^2 \gg \mathcal{H} m a$): Wave-like effects dominate, with a nonzero effective sound speed $c_s^2 \sim k^2/(m^2 a^2)$. The power spectrum is suppressed on small scales (below the Jeans scale), with density perturbations oscillating or decaying, and anisotropic stress becomes significant.
• Early Universe regime ($m \ll H$): The field's energy density scales as radiation ($w = 1/3$) (Flambaum et al., 2019). When $m a \sim \mathcal{H}$, the field transitions to behaving as CDM, with $w \to 0$ and $\rho_A \propto a^{-3}$.

UVDM in an anisotropic Bianchi I universe naturally sources metric shear ($\sigma_{ij}$). Correctly accounting for the shear is essential for establishing consistent cosmological adiabatic initial conditions and avoiding spurious infrared (IR) effects in perturbation evolution (Chase et al., 2023, Chase et al., 22 Aug 2024).

2. Production Mechanisms and Abundance

The expected relic abundance and phase-space structure of UVDM are strongly shaped by its production:

• Parametric Resonance (PR) from Dark Higgs: If the vector mass arises from a symmetry-breaking dark Higgs field with large post-inflationary displacement, efficient nonthermal production can occur via parametric resonance. This mechanism preferentially amplifies longitudinal modes, with the mass as low as $m \gtrsim 10^{-18}$ eV being allowed when $e\gg \lambda$, where $e$ and $\lambda$ are the gauge and quartic couplings, respectively (Dror et al., 2018).
• Inflation-Induced Fluctuations: Direct production during inflation is feasible if the longitudinal mode of the vector field acquires fluctuations due to a rapidly changing mass (non-slowroll phase), typically parameterized by a function $J(\tau)$ in the time-dependent mass term, $M^2(\tau) = m^2 J^2(\tau)/a^2(\tau)$ (Rosa et al., 22 Aug 2025). This scenario links ultralight vector DM generation to the dynamics pertinent in primordial black hole production.
• Kinetic Misalignment and Freeze-In: Analogously to scalar misalignment, the vector field's initial value set during inflation leads to nonthermal abundance. However, the necessary initial value and abundance depend on the vector mass and early-universe evolution (Dror et al., 2018).

The PR mechanism generically yields a dominant longitudinal population and may be accompanied by dark Higgs remnant signals, cosmic string formation (with $G\mu$ constrained by CMB and gravitational-wave searches), and isocurvature perturbation constraints.

3. Cosmological and Astrophysical Signatures

3.1 Structure Formation and Anisotropies

UVDM generically predicts:

• Small-scale suppression: The matter power spectrum is suppressed on scales $$k \gtrsim k_J \sim a_\mathrm{osc} \sqrt{m H_\mathrm{osc}}$$ (Jeans scale), similarly to ultralight scalar dark matter (Chase et al., 22 Aug 2024).
• Power anisotropy: For a background vector field aligned in a fixed spatial direction, the suppression amplitude of the power spectrum depends on $\gamma_k$, the angle between the Fourier mode and the vector direction. Anisotropic features:

$$P(k, \gamma_k) = P(k, \pi/2)[1-g(k)\cos^4\gamma_k],$$

are absent in scalar fuzzy dark matter, representing a distinctive vector imprint (Chase et al., 22 Aug 2024).

• Particle regime: On large scales, adiabatic initial conditions recover standard $\Lambda$CDM. In the Bianchi I background, the inclusion of the metric shear exactly cancels leading-order anisotropic terms, ensuring standard adiabatic evolution (Chase et al., 2023).

3.2 Pulsar Timing Arrays (PTAs)

PTAs can probe UVDM via induced monochromatic timing residuals of frequency $f \simeq m/\pi$ for $m \sim 10^{-24} - 10^{-22}$ eV (Nomura et al., 2019, Unal et al., 2022, Wu et al., 2022, Omiya et al., 2023, Dror et al., 28 May 2025, Nomura et al., 10 Aug 2025):

• Amplitude and Angular Dependence: For vector DM, the residual amplitude is predicted to be three times larger than for scalar DM, and exhibits a unique angular modulation (e.g., through $1 + 3\cos2\theta$) and dependence on polarization structure (Nomura et al., 2019, Wu et al., 2022, Nomura et al., 10 Aug 2025).
• Correlation Curve: The cross-correlation of timing residuals between pulsar pairs deviates from the standard Hellings–Downs curve (SGWB): UVDM generally produces a monopole-quadrupole structure, with pronounced quadrupole (P$_2$) term for circular polarization (Omiya et al., 2023, Nomura et al., 10 Aug 2025).
• Statistical Framework: A complete statistical treatment considers both fast (coherent oscillations) and slow (interference) modes, with equipartition among polarization states (Dror et al., 28 May 2025).
• Finite Velocity Effects: Including finite DM velocity, velocity-suppressed (divergent as $1/v^2$) terms dominate the amplitude, making the distinction between vector and scalar timing signals challenging unless polarization or angular correlations are measured for distant pulsar pairs (Zhu, 30 Sep 2024).

3.3 Gravitational-wave Propagation

• Anisotropic Damping: Coherent background UVDM modifies the propagation equation for gravitational waves, inducing anisotropic suppression of tensor amplitude—maximal for propagation perpendicular to the vector direction (Miravet et al., 2020). The effect is negligible for astrophysical GW sources but can lead to observable suppression for primordial GWs entering the horizon near the onset of field oscillations, potentially accessible via precise CMB B-mode polarization data (e.g., LiteBIRD).
• Gravitational Slip and Tensor-to-Scalar Ratio: In the wave regime, nonzero anisotropic stress produces a gravitational slip $(\Phi-\Psi)/\Phi \sim c_s^2$ and a nonvanishing tensor-to-scalar mode ratio $h/\Phi \sim c_s^2$; for small scales $k \gg m a$ these features distinguish vector from scalar dark matter models, although the predicted gravitational-wave background remains below current detector sensitivities (Cembranos et al., 2016).

4. Experimental Searches and Detection Strategies

4.1 Interferometric and Quantum Sensors

• Force Detection: Precision experiments such as the KAGRA gravitational-wave detector search for UVDM by detecting oscillating, coherent forces exerted on suspended mirrors due to vector–matter couplings (e.g., $U(1)_{B-L}$). The induced force amplitude is material-dependent, e.g., $$a_\mathrm{DM}(t) = g_{B-L}a_0[(A-Z)/A]\sin(m_\mathrm{DM} t)$$ (Antypas et al., 2022, Michimura et al., 2021, Collaboration et al., 5 Mar 2024, Michimura et al., 15 Jan 2025), and manifests as differential arm-length changes (Michimura et al., 2021, Michimura et al., 15 Jan 2025).
• Auxiliary Channels and Material Differentiation: KAGRA implements auxiliary interferometric channels involving both sapphire and fused silica mirrors, exploiting slight differences in B–L charge-to-mass ratios to enhance signal sensitivity (Collaboration et al., 5 Mar 2024).
• Terrestrial Quantum Sensors: Optomechanical accelerometers, atomic interferometers, and related quantum devices perform sensitive searches for UVDM. Due to equipartition among the three vector polarizations, the laboratory signal traces a “random ellipse” in the coherent regime, yielding a characteristic three-peak signature in the frequency spectrum—at $m$, $m \pm \Omega_\oplus$ (Earth’s rotation frequency)—allowing latitude-independent constraints (Amaral et al., 4 Mar 2024).
• Distinction from Scalar DM: These methods can exploit the vector’s composition and directionality, especially through modulations caused by the Earth’s rotation or by comparing test masses made of different elements (Antypas et al., 2022, Amaral et al., 4 Mar 2024).

4.2 Astrophysical and Cosmological Probes

• Pulsar Timing Arrays: Constraints on the UVDM density using the absence of monochromatic timing residuals reach $\rho_{\mathrm{VF}} \lesssim 5$ GeV/cm$^3$ for $m \lesssim 10^{-23}$ eV (Wu et al., 2022). PTA analysis includes Bayesian inference pipelines accounting for the vector field’s direction and polarization.
• Cosmic Expansion and the Hubble Tension: Early-universe UVDM may act as “dark radiation” ($w=1/3$) before transitioning to CDM-like ($w=0$) at $t \sim m^{-1}$, reducing the BAO sound horizon and raising the locally inferred $H_0$—potentially resolving the Hubble tension (Flambaum et al., 2019).
• CMB B-mode Polarization: Anisotropic suppression of primordial GW power due to UVDM may be probed with next-generation B-mode experiments (LiteBIRD), with detectability for $m \lesssim 10^{-26}$ eV and sufficient energy density (Miravet et al., 2020).
• Nonminimal Gravity Couplings: UVDM with nonminimal couplings to curvature can alter the propagation speed of GWs—constrained with high precision using GW170817 and corresponding electromagnetic signals (Zhang, 2023).

5. Distinctive Properties, Polarization, and Identification Strategies

• Vectorial and Polarization Signatures: UVDM time-averaged energy density is isotropic in the absence of preferred direction. However, a nontrivial polarization structure (linear, elliptical, circular) further imprints on observables. Circular polarization enhances the quadrupole structure of the PTA angular correlation curve, resulting in a more pronounced deformation of the classic Hellings–Downs curve, while linear polarization preserves a stronger monopole (Nomura et al., 10 Aug 2025).
• Statistical Treatment: Signal analysis in both laboratory and astrophysical contexts must account for the vector's stochastic amplitude and polarization distribution (see the $\mathcal{P}$-representation for field amplitudes), yielding statistically isotropic covariances in the case of equipartition, but with nontrivial angular dependencies in cross-correlations (Dror et al., 28 May 2025).
• Distinguishability from Scalar Fuzzy Dark Matter: While the suppression scale is similar, UVDM can be uniquely identified through
  • Power spectrum anisotropy in LSS/21cm analyses (Chase et al., 22 Aug 2024),
  • Polarization-dependent, angle-varying timing residuals in PTAs (Nomura et al., 2019, Omiya et al., 2023, Nomura et al., 10 Aug 2025),
  • Three-peak signals in terrestrial time-series experiments (Amaral et al., 4 Mar 2024),
  • Unique gravitational slip and tensor-to-scalar ratio scaling in cosmological perturbations (Cembranos et al., 2016).

6. Implications, Open Challenges, and Outlook

UVDM models provide an extensive phenomenological landscape for probing physics beyond the Standard Model and the early universe:

• Parameter Space Coverage: A broad mass window ($10^{-28}$ eV $\lesssim m \lesssim$ few eV) is compatible with current constraints, motivating complementary searches using laboratory, astrophysical, and cosmological techniques (Antypas et al., 2022).
• Multi-Component/Mixed Scenarios: Production mechanisms tied to non-slowroll inflationary epochs naturally relate ultralight vector dark matter to primordial black hole formation, allowing mixed dark matter scenarios to be embedded within a single dynamical origin (Rosa et al., 22 Aug 2025).
• Distinct Gravitational-Wave Backgrounds: Second-order production of gravitational waves from non-adiabatic vector fluctuations predicts low-frequency stochastic backgrounds, potentially distinguishable from astrophysical sources in CMB or alternative GW observables (Rosa et al., 22 Aug 2025).
• Experimental Prospects: Next-generation PTAs (e.g., SKA), improved mechanical and atomic sensors, and enhanced interferometric runs (e.g., future KAGRA cycles), are expected to further probe the allowed UVDM parameter space, possibly reaching sensitivity to dark matter fractions at the $10^{-3}$–$10^{-2}$ level (Unal et al., 2022).

The detection or exclusion of UVDM thus requires leveraging a suite of experimental channels—PTAs for polarization-resolved residuals, laboratory sensors exploiting the polarization/anisotropic imprint, and cosmological probes of tensor and scalar perturbations—to fully exploit the rich phenomenology associated with this non-scalar alternative to cold dark matter.