Scalar Ultralight Dark Matter: Theory & Experiments

• Scalar ULDM is a model where ultralight spin-0 bosons form a coherent classical field, influencing galactic dynamics and small-scale structures.
• The theory employs Schrödinger–Poisson dynamics to describe solitonic cores and modified halo profiles that may address core–cusp issues.
• Precision experiments like pulsar timing, interferometry, and neutrino detectors probe ULDM through oscillatory variations and direct Standard Model couplings.

Scalar ultralight dark matter (ULDM) denotes dark-matter scenarios in which the dark sector is carried by spin-0 bosons with masses from $10^{-24}\,\mathrm{eV}$ up to the eV scale, with particular phenomenological interest in $10^{-24}\,\mathrm{eV}<m<1\,\mathrm{eV}$ and especially $m\sim10^{-22}\,\mathrm{eV}$, where the de Broglie wavelength becomes macroscopic on galactic scales (Ferreira, 2020). In this regime the field is typically treated as a coherent classical wave or condensate, so its phenomenology spans self-gravitating solitons, suppression of small-scale structure, oscillatory variations of masses and fundamental constants, and precision signatures in clocks, interferometers, pulsar timing, orbital dynamics, and neutrino oscillations. Recent work has extended the canonical single-field picture to include self-interactions, multifield configurations, direct couplings to Standard Model sectors and neutrinos, and cosmological scenarios in which ULDM constitutes either all or only a fraction of the total dark matter abundance.

1. Wave mechanics and classical-field description

A central feature of scalar ULDM is that, for sufficiently small mass, galactic phase-space occupation numbers are enormous, justifying a classical-field description. In the review literature this appears as Bose–Einstein condensation or superfluid behavior on galactic scales, with the dark matter described by a macroscopic wavefunction $\psi(\mathbf r,t)$ obeying Schrödinger–Poisson or Gross–Pitaevskii–Poisson dynamics rather than an $N$-body particle description (Ferreira, 2020). In the nonrelativistic, weak-field limit with quartic self-interaction, one widely used form is

$$i \frac{\partial \Psi}{\partial t} = -\frac{\nabla^2}{2m} \Psi + m \Phi \Psi + \frac{\lambda}{8 m^3} |\Psi|^2 \Psi, \qquad \nabla^2 \Phi = 4\pi G |\Psi|^2,$$

which governs self-gravitating scalar configurations and their stationary solitonic solutions (Dave, 30 Dec 2025).

The same wave description underlies the characteristic suppression of structure below a Jeans-like scale. In linear theory the matter power spectrum is modified as

$P_{\rm ULDM}(k,z)=T^2(k,z)\,P_{\rm CDM}(k,z),$

with the transfer function $T(k,z)$ encoding the small-scale cutoff induced by quantum pressure (Ferreira, 2020). In hydrodynamical language, the quantum-pressure term opposes gravitational collapse on small scales, producing cored inner density distributions and a minimum halo scale. This mechanism is one of the standard motivations for ULDM as an alternative to collisionless CDM on sub-galactic scales (Ferreira, 2020).

Local observables are commonly phrased in terms of an oscillating background scalar. In direct-coupling analyses the field is written as a coherent oscillation such as

$\phi(t)=\phi_0 \sin(m_\phi t),$

or, including stochastic local amplitude and phase,

$$\Phi = \frac{\sqrt{2\rho_{\rm DM}}}{m}\,\varrho\,\cos(mt+\Upsilon),$$

reflecting the coherent classical-wave picture on scales small compared with the de Broglie wavelength (Delgadillo et al., 20 Dec 2025). This oscillatory background is the common origin of the time-domain signals sought in laboratory experiments, timing arrays, and neutrino facilities.

2. Solitons, halo structure, and self-interactions

In the standard single-field picture, astrophysically realistic ULDM halos are expected to consist of an inner solitonic core embedded in an outer NFW-like halo (Kendall et al., 2019). A representative parameterization is piecewise, with $10^{-24}\,\mathrm{eV}<m<1\,\mathrm{eV}$0 inside a transition radius $10^{-24}\,\mathrm{eV}<m<1\,\mathrm{eV}$1 and $10^{-24}\,\mathrm{eV}<m<1\,\mathrm{eV}$2 outside, while simulation-motivated core–halo relations connect the core density and radius to the virial halo mass. One form quoted in the literature is

$10^{-24}\,\mathrm{eV}<m<1\,\mathrm{eV}$3

with $10^{-24}\,\mathrm{eV}<m<1\,\mathrm{eV}$4 (Kendall et al., 2019). The inverse mass–radius scaling of the soliton implies that more massive cores are smaller and denser.

That scaling is the basis of an important controversy. Although ULDM is often invoked as a resolution of the core–cusp problem, detailed profile comparisons show that ULDM halos need not be systematically less cuspy than their NFW counterparts. For halos up to $10^{-24}\,\mathrm{eV}<m<1\,\mathrm{eV}$5, feasible ULDM profiles exist whose central density is lower than NFW at astrophysically accessible radii, but observed profiles do not strongly favor either option; both ULDM and NFW can fit subsets of the data for some parameter choices (Kendall et al., 2019). At higher halo masses the solitonic core can become so concentrated that ULDM may exacerbate rather than alleviate the central-density tension. This makes the claim that ULDM universally solves the core–cusp problem untenable in its simplest form (Kendall et al., 2019).

Self-interactions substantially broaden the phenomenology. In the nonrelativistic limit a quartic interaction $10^{-24}\,\mathrm{eV}<m<1\,\mathrm{eV}$6 modifies the soliton structure: repulsive interactions ($10^{-24}\,\mathrm{eV}<m<1\,\mathrm{eV}$7) produce larger, lower-density cores and can enter a Thomas–Fermi regime, while attractive interactions ($10^{-24}\,\mathrm{eV}<m<1\,\mathrm{eV}$8) yield smaller, denser configurations and a maximum stable mass,

$10^{-24}\,\mathrm{eV}<m<1\,\mathrm{eV}$9

beyond which dilute solitons collapse (Dave, 30 Dec 2025). Astrophysical constraints reach extremely small couplings. Using the upper limit on the dark matter mass within $m\sim10^{-22}\,\mathrm{eV}$0 pc of M87, analyses probe $m\sim10^{-22}\,\mathrm{eV}$1; for $m\sim10^{-22}\,\mathrm{eV}$2, self-couplings of order $m\sim10^{-22}\,\mathrm{eV}$3 are accessible, and if ultralight axions form all of dark matter the mass is constrained to be less than $m\sim10^{-22}\,\mathrm{eV}$4 in that framework (Chakrabarti et al., 2022). In low-surface-brightness galaxies, repulsive self-interactions with $m\sim10^{-22}\,\mathrm{eV}$5 and $m\sim10^{-22}\,\mathrm{eV}$6 can simultaneously accommodate observed rotation curves and an empirical soliton–halo mass relation, whereas the non-interacting case cannot do so in the cited analysis (Dave, 30 Dec 2025). Attractive interactions also alter environmental stability: for satellite dwarfs, they can extend lifetimes over cosmological timescales and reopen parameter space excluded in the non-interacting case; for Fornax-like conditions, survival at $m\sim10^{-22}\,\mathrm{eV}$7 requires $m\sim10^{-22}\,\mathrm{eV}$8 in the quoted study (Dave, 30 Dec 2025).

The single-field picture is itself not mandatory. In “multifield ULDM,” the halo is built from $m\sim10^{-22}\,\mathrm{eV}$9 gravitationally interacting but otherwise independent scalar fields. Simulations and analytic estimates show that the amplitude of the total density fluctuations decreases as $\psi(\mathbf r,t)$0, the two-point correlation function scales as $\psi(\mathbf r,t)$1, and the constituent fields do not become significantly correlated over cosmological timescales (Gosenca et al., 2023). Since stellar heating depends on halo granularity, the induced stellar velocity dispersion scales as $\psi(\mathbf r,t)$2 for $\psi(\mathbf r,t)$3 equal-mass fields and as $\psi(\mathbf r,t)$4 when a much lighter field $\psi(\mathbf r,t)$5 dominates the heating (Gosenca et al., 2023). This weakens stellar-dispersion bounds relative to the single-field case and implies that astrophysical limits derived for canonical fuzzy-DM halos need not transfer directly to multifield realizations.

3. Couplings to Standard Model sectors and neutrinos

Beyond purely gravitational effects, scalar ULDM may couple directly to Standard Model operators. A representative dilaton-like interaction used in pulsar-timing analyses is

$\psi(\mathbf r,t)$6

with $\psi(\mathbf r,t)$7 and dimensionless couplings $\psi(\mathbf r,t)$8 (Wu et al., 2024). Such couplings induce oscillations of $\psi(\mathbf r,t)$9, $N$0, quark masses, pulsar spin rates, and reference-clock frequencies. In optical-cavity language, the relevant variations are commonly parameterized as

$N$1

leading to a cavity strain

$N$2

that can be read out as beat-frequency oscillations between stabilized lasers (Deshpande et al., 2024).

Neutrino-sector couplings define a distinct phenomenology. In one formulation,

$N$3

so the effective mass-squared splittings become periodically modulated,

$N$4

Here $N$5 quantifies the relative modulation of $N$6 by the ULDM background (Delgadillo et al., 20 Dec 2025). When the detector integration time is much longer than the ULDM oscillation period, the rapid modulation averages into an additional smearing of neutrino oscillation features. The resulting probability distortion is decoherence-like rather than a resolved sideband structure, and it can bias the extraction of oscillation parameters (Delgadillo et al., 20 Dec 2025).

These coupling scenarios also expose a model-building issue. Quadratically coupled scalar ULDM is experimentally attractive, but generic scalar masses are radiatively unstable. In one recent proposal the scalar is realized as a pseudo-Nambu–Goldstone boson coupled quadratically to both the Standard Model and a twin copy related by mirror $N$7 symmetry; the leading radiative correction, linear in the coupling, cancels, leaving a correction quadratic in the tiny coupling (Delaunay et al., 16 Jul 2025). This construction was proposed specifically to make experimentally accessible quadratically coupled ULDM natural over a much larger parameter region (Delaunay et al., 16 Jul 2025).

4. Precision experiments and detector concepts

Several experimental programs target the oscillatory signatures of scalar ULDM in controlled detectors. Broadband atom gradiometers are designed to probe linearly coupled scalar ULDM over frequencies from approximately $N$8 to $N$9, but signals above the Nyquist frequency are aliased, producing folding, distortion, and discrete “islands” in reconstructed parameter space (Badurina et al., 2023). A likelihood-based analysis showed that accurate reconstruction remains possible provided the experimental frequency resolution is larger than the ULDM signal linewidth, and more conservatively when the resolution is at least five times better than the linewidth (Badurina et al., 2023). For compact interferometers, refined treatments of the scalar signal in vertical gradiometers introduce a suppression factor $$i \frac{\partial \Psi}{\partial t} = -\frac{\nabla^2}{2m} \Psi + m \Phi \Psi + \frac{\lambda}{8 m^3} |\Psi|^2 \Psi, \qquad \nabla^2 \Phi = 4\pi G |\Psi|^2,$$0 that is especially important for short baselines. In the AION-10 case, this correction lowers naive sensitivity estimates but still leaves access to previously unconstrained scalar–electron coupling parameter space around $$i \frac{\partial \Psi}{\partial t} = -\frac{\nabla^2}{2m} \Psi + m \Phi \Psi + \frac{\lambda}{8 m^3} |\Psi|^2 \Psi, \qquad \nabla^2 \Phi = 4\pi G |\Psi|^2,$$1–$$i \frac{\partial \Psi}{\partial t} = -\frac{\nabla^2}{2m} \Psi + m \Phi \Psi + \frac{\lambda}{8 m^3} |\Psi|^2 \Psi, \qquad \nabla^2 \Phi = 4\pi G |\Psi|^2,$$2, with broadband operation generally more advantageous than resonant mode in the cited study (Badurina et al., 2021).

Cryogenic optical cavities provide a complementary high-frequency laboratory probe. A tabletop experiment based on two sapphire Fabry–Perot cavities at $$i \frac{\partial \Psi}{\partial t} = -\frac{\nabla^2}{2m} \Psi + m \Phi \Psi + \frac{\lambda}{8 m^3} |\Psi|^2 \Psi, \qquad \nabla^2 \Phi = 4\pi G |\Psi|^2,$$3 K searched for differential length oscillations over Compton frequencies from $$i \frac{\partial \Psi}{\partial t} = -\frac{\nabla^2}{2m} \Psi + m \Phi \Psi + \frac{\lambda}{8 m^3} |\Psi|^2 \Psi, \qquad \nabla^2 \Phi = 4\pi G |\Psi|^2,$$4 to $$i \frac{\partial \Psi}{\partial t} = -\frac{\nabla^2}{2m} \Psi + m \Phi \Psi + \frac{\lambda}{8 m^3} |\Psi|^2 \Psi, \qquad \nabla^2 \Phi = 4\pi G |\Psi|^2,$$5, with primary sensitivity in a $$i \frac{\partial \Psi}{\partial t} = -\frac{\nabla^2}{2m} \Psi + m \Phi \Psi + \frac{\lambda}{8 m^3} |\Psi|^2 \Psi, \qquad \nabla^2 \Phi = 4\pi G |\Psi|^2,$$6–$$i \frac{\partial \Psi}{\partial t} = -\frac{\nabla^2}{2m} \Psi + m \Phi \Psi + \frac{\lambda}{8 m^3} |\Psi|^2 \Psi, \qquad \nabla^2 \Phi = 4\pi G |\Psi|^2,$$7 science band bounded by cavity mechanical resonances near $$i \frac{\partial \Psi}{\partial t} = -\frac{\nabla^2}{2m} \Psi + m \Phi \Psi + \frac{\lambda}{8 m^3} |\Psi|^2 \Psi, \qquad \nabla^2 \Phi = 4\pi G |\Psi|^2,$$8 and $$i \frac{\partial \Psi}{\partial t} = -\frac{\nabla^2}{2m} \Psi + m \Phi \Psi + \frac{\lambda}{8 m^3} |\Psi|^2 \Psi, \qquad \nabla^2 \Phi = 4\pi G |\Psi|^2,$$9 (Deshpande et al., 2024). Using a 4-day time series sampled every $P_{\rm ULDM}(k,z)=T^2(k,z)\,P_{\rm CDM}(k,z),$0, the analysis found no ULDM signal and set new direct limits on $P_{\rm ULDM}(k,z)=T^2(k,z)\,P_{\rm CDM}(k,z),$1, improving previous direct bounds by $P_{\rm ULDM}(k,z)=T^2(k,z)\,P_{\rm CDM}(k,z),$2–$P_{\rm ULDM}(k,z)=T^2(k,z)\,P_{\rm CDM}(k,z),$3 orders of magnitude in the $P_{\rm ULDM}(k,z)=T^2(k,z)\,P_{\rm CDM}(k,z),$4–$P_{\rm ULDM}(k,z)=T^2(k,z)\,P_{\rm CDM}(k,z),$5 range for a standard halo model. For an Earth-bound relaxion-star model, the higher assumed local density improves sensitivity by $P_{\rm ULDM}(k,z)=T^2(k,z)\,P_{\rm CDM}(k,z),$6 orders of magnitude relative to the standard halo case (Deshpande et al., 2024).

Large liquid scintillator detectors can search for ULDM through neutrino oscillations rather than clock or interferometric observables. A JUNO-like simulation with GLoBES for a $P_{\rm ULDM}(k,z)=T^2(k,z)\,P_{\rm CDM}(k,z),$7 kton detector, $P_{\rm ULDM}(k,z)=T^2(k,z)\,P_{\rm CDM}(k,z),$8 years of exposure at $P_{\rm ULDM}(k,z)=T^2(k,z)\,P_{\rm CDM}(k,z),$9 GW reactor power, and JUNO systematics projected $T(k,z)$0 C.L. bounds

$T(k,z)$1

in the time-averaged modulation regime (Delgadillo et al., 20 Dec 2025). In that study the effect modestly degrades the precision of $T(k,z)$2 and $T(k,z)$3, leaves the solar sector comparatively unaffected, and can reduce the mass-ordering sensitivity $T(k,z)$4 by up to $T(k,z)$5 units in the quoted scenario (Delgadillo et al., 20 Dec 2025).

Space-based gravitational-wave detectors introduce a further channel. In LISA, scalar ULDM coupled to Standard Model fields produces oscillatory test-mass accelerations and hence Doppler shifts in exchanged laser light. The response is quasi-monochromatic, but it is not degenerate with a quasi-monochromatic gravitational wave: in the long-wavelength limit the $T(k,z)$6-channel transfer functions scale as $T(k,z)$7 for scalar ULDM and $T(k,z)$8 for gravitational waves (Gué et al., 19 Aug 2025). Using one year of realistic LISA orbits and Bayesian model selection, the cited analysis found no substantial degeneracy and concluded that LISA should be able to discriminate a scalar ULDM signal from a gravitational-wave signal in practice (Gué et al., 19 Aug 2025).

5. Timing, orbital dynamics, and gravitational-wave probes

Pulsar timing arrays (PTAs) are sensitive both to the oscillatory gravitational potential sourced by ULDM and to direct coupling effects. In the European PTA second data release, a Bayesian analysis of 25 pulsars spanning 24.7 years searched the mass range $T(k,z)$9 and found no significant detection, with $\phi(t)=\phi_0 \sin(m_\phi t),$0 for the sinusoidal signals considered (Wu et al., 2024). The same work derived upper limits on $\phi(t)=\phi_0 \sin(m_\phi t),$1, reported stronger coupling constraints than earlier PTA experiments, and found particularly strong sensitivity to the muon coupling $\phi(t)=\phi_0 \sin(m_\phi t),$2, improving previous astrophysical limits by three orders of magnitude because neutron stars contain large numbers of muons (Wu et al., 2024). It also stated that EPTA DR2 alone rules out 100% ULDM in the local density for $\phi(t)=\phi_0 \sin(m_\phi t),$3 based solely on gravitational effects (Wu et al., 2024).

A separate Bayesian study using PPTA-DR3 together with EPTA-DR2 reached a different exclusion statement for the scalar gravitational signal: no statistically significant evidence for ULDM was found, and the resulting $\phi(t)=\phi_0 \sin(m_\phi t),$4 C.L. limits do not exclude the scenario in which scalar ULDM constitutes all of dark matter (Hu et al., 4 May 2026). In that analysis the scalar signal amplitude was modeled with pulsar-distance priors and a soliton-plus-NFW Galactic density profile, and PPTA-DR3 improved over PPTA-DR2 by factors of $\phi(t)=\phi_0 \sin(m_\phi t),$5 for $\phi(t)=\phi_0 \sin(m_\phi t),$6, by $\phi(t)=\phi_0 \sin(m_\phi t),$7–$\phi(t)=\phi_0 \sin(m_\phi t),$8 at $\phi(t)=\phi_0 \sin(m_\phi t),$9–$$\Phi = \frac{\sqrt{2\rho_{\rm DM}}}{m}\,\varrho\,\cos(mt+\Upsilon),$$0, and by $$\Phi = \frac{\sqrt{2\rho_{\rm DM}}}{m}\,\varrho\,\cos(mt+\Upsilon),$$1 for $$\Phi = \frac{\sqrt{2\rho_{\rm DM}}}{m}\,\varrho\,\cos(mt+\Upsilon),$$2 (Hu et al., 4 May 2026). The coexistence of these results indicates that current PTA exclusions remain analysis-dependent, particularly with respect to correlated versus uncorrelated treatments, noise modeling, and density assumptions.

Binary pulsars probe direct matter couplings through orbital osculation. Extending a two-step Bayesian framework originally built for linearly coupled scalar ULDM, one recent analysis derived new constraints on quadratic scalar coupling $$\Phi = \frac{\sqrt{2\rho_{\rm DM}}}{m}\,\varrho\,\cos(mt+\Upsilon),$$3 in the mass interval $$\Phi = \frac{\sqrt{2\rho_{\rm DM}}}{m}\,\varrho\,\cos(mt+\Upsilon),$$4 to $$\Phi = \frac{\sqrt{2\rho_{\rm DM}}}{m}\,\varrho\,\cos(mt+\Upsilon),$$5, a regime described there as inaccessible to other experiments (Huxhagen et al., 28 Apr 2026). The sensitivity is dominated by the orbital phase $$\Phi = \frac{\sqrt{2\rho_{\rm DM}}}{m}\,\varrho\,\cos(mt+\Upsilon),$$6 at lower masses and by the projected semi-major axis $$\Phi = \frac{\sqrt{2\rho_{\rm DM}}}{m}\,\varrho\,\cos(mt+\Upsilon),$$7 at higher masses, while eccentric binaries develop resonance structure. Simulated-data studies using autoencoders and convolutional classifiers reached sensitivities comparable to a semi-analytical Bayesian approach for the linear scalar case and could distinguish linear and quadratic scalar signals from vector and tensor ULDM in multiclass mode, albeit with some loss of optimality relative to the Bayesian benchmark (Kůs et al., 4 Jun 2025).

Stellar and black-hole orbital dynamics provide another set of precision probes. In the Galactic Center, quadratic scalar coupling induces a non-oscillatory perturbation and long-term secular orbital evolution for S-stars. Using the observed periastron precession of S2, one study constrained the ULDM-to-Sgr A$$\Phi = \frac{\sqrt{2\rho_{\rm DM}}}{m}\,\varrho\,\cos(mt+\Upsilon),$$8 mass ratio to $$\Phi = \frac{\sqrt{2\rho_{\rm DM}}}{m}\,\varrho\,\cos(mt+\Upsilon),$$9 for a $10^{-24}\,\mathrm{eV}<m<1\,\mathrm{eV}$00 gravitational-atom state at $10^{-24}\,\mathrm{eV}<m<1\,\mathrm{eV}$01, and to $10^{-24}\,\mathrm{eV}<m<1\,\mathrm{eV}$02 for a spherical soliton extending to $10^{-24}\,\mathrm{eV}<m<1\,\mathrm{eV}$03 pc at $10^{-24}\,\mathrm{eV}<m<1\,\mathrm{eV}$04 (Yu et al., 9 Apr 2026). The same analysis found that the resulting bounds on the quadratic coupling surpass current limits in the mass range $10^{-24}\,\mathrm{eV}<m<1\,\mathrm{eV}$05 (Yu et al., 9 Apr 2026).

ULDM also affects the gravitational-wave background indirectly through supermassive black-hole binaries embedded in solitonic halos. Semi-analytic models of ULDM-enhanced drag show that dense central solitons accelerate inspiral, shorten merger times, and suppress low-frequency gravitational radiation. Fitting PTA data to this mechanism yielded a median ULDM particle mass of $10^{-24}\,\mathrm{eV}<m<1\,\mathrm{eV}$06 in a “pinched soliton” model, with drag efficiency scaling as $10^{-24}\,\mathrm{eV}<m<1\,\mathrm{eV}$07 in a simpler unpinched model (Tiruvaskar et al., 17 Dec 2025). In that framework the mass is better constrained than the ULDM fraction, suggesting that even subdominant ULDM components can affect SMBH merger dynamics (Tiruvaskar et al., 17 Dec 2025).

6. Cosmology, production, naturalness, and unresolved issues

Early-universe analyses divide naturally into production and constraint problems. Under minimal assumptions—a free real scalar spectator in the Bunch–Davies vacuum during inflation followed by instantaneous reheating—non-adiabatic gravitational production yields a distribution function

$10^{-24}\,\mathrm{eV}<m<1\,\mathrm{eV}$08

at low comoving momentum for minimally coupled ULDM (Herring et al., 2019). This infrared enhancement is inherited from inflationary superhorizon mode amplification. For an inflationary scale $10^{-24}\,\mathrm{eV}<m<1\,\mathrm{eV}$09, the resulting relic saturates the dark-matter abundance at $10^{-24}\,\mathrm{eV}<m<1\,\mathrm{eV}$10, with equation-of-state parameter $10^{-24}\,\mathrm{eV}<m<1\,\mathrm{eV}$11 and free-streaming length $10^{-24}\,\mathrm{eV}<m<1\,\mathrm{eV}$12, i.e. a cold dark matter relic despite its tiny mass (Herring et al., 2019). The authors argue that this mechanism furnishes a lower bound on the abundance of generic minimally coupled ultralight scalars and axion-like particles (Herring et al., 2019).

Cosmological constraints tighten considerably when the scalar quadratically modulates fundamental constants. A self-consistent treatment of ULDM-induced variations in $10^{-24}\,\mathrm{eV}<m<1\,\mathrm{eV}$13 and $10^{-24}\,\mathrm{eV}<m<1\,\mathrm{eV}$14 during BBN and recombination, implemented in a modified Boltzmann code and fit to Planck 2018, SPT-3G, and BAO data, found that for $10^{-24}\,\mathrm{eV}<m<1\,\mathrm{eV}$15 the allowed ULDM fraction is more constrained than in pure ULDM models, and for $10^{-24}\,\mathrm{eV}<m<1\,\mathrm{eV}$16 the CMB limits on the variational couplings are stronger than those derived from primordial helium abundance alone (Ghosh et al., 18 Nov 2025). In the high-mass regime $10^{-24}\,\mathrm{eV}<m<1\,\mathrm{eV}$17, the main effect is through the BBN-modified helium abundance, with quoted $10^{-24}\,\mathrm{eV}<m<1\,\mathrm{eV}$18 C.L. bounds $10^{-24}\,\mathrm{eV}<m<1\,\mathrm{eV}$19 from Planck alone and $10^{-24}\,\mathrm{eV}<m<1\,\mathrm{eV}$20 from Planck+BAO+SPT (Ghosh et al., 18 Nov 2025). The same analysis concluded that, within the quadratic ULDM model considered, variation of fundamental constants has no appreciable impact on the Hubble constant inferred from the CMB and therefore does not solve the Hubble tension (Ghosh et al., 18 Nov 2025).

Several broader issues remain unsettled. First, the halo phenomenology is not captured by a single universal profile prescription: multifield models smooth granularity and weaken stellar-heating bounds (Gosenca et al., 2023), while self-interactions can either rescue or destabilize parts of parameter space depending on sign and magnitude (Dave, 30 Dec 2025). Second, precision-search interpretations are not yet uniform, as illustrated by the contrast between PTA studies that report exclusion of all-DM scalar ULDM over part of the $10^{-24}\,\mathrm{eV}<m<1\,\mathrm{eV}$21–$10^{-24}\,\mathrm{eV}<m<1\,\mathrm{eV}$22 range and others that find the all-DM scenario still allowed (Wu et al., 2024). Third, naturalness is nontrivial for directly coupled scalars, motivating symmetry-based constructions such as the mirror $10^{-24}\,\mathrm{eV}<m<1\,\mathrm{eV}$23 “quadratic twin” mechanism (Delaunay et al., 16 Jul 2025). Finally, the broad ULDM program still faces the same empirical requirement emphasized in work on the core–cusp problem: robust discrimination among ULDM, CDM, and baryon-modified alternatives will require more comprehensive observations and simulations that include baryonic feedback (Kendall et al., 2019).

In that sense scalar ULDM is best regarded not as a single model but as a structured class of theories. Its defining features are a coherent classical scalar field, a halo phenomenology set by wave mechanics and possible self-interactions, and a distinctive capacity to imprint oscillatory or secular signatures across experiments that span optical cavities, atom interferometers, liquid scintillator neutrino detectors, pulsar timing, Galactic Center dynamics, and the gravitational-wave sky. The diversity of current constraints already excludes large regions of parameter space, but the surviving landscape depends sensitively on field multiplicity, coupling structure, environmental dynamics, and cosmological history.