FIMPs: Feebly Interacting Massive Particles

• FIMPs are dark-matter candidates with extremely weak couplings that never reach thermal equilibrium, produced via freeze-in processes.
• They achieve nonthermal relic abundances through decays and scatterings, providing unique insights into early-Universe cosmology.
• FIMP models predict observable signals in collider experiments and indirect searches via long-lived mediators and portal interactions.

Feebly Interacting Massive Particles (FIMPs) are dark-matter candidates whose coupling to the visible sector is so small that they never reach thermal equilibrium with the Standard Model plasma. Their relic abundance is generated non-thermally, typically by freeze-in: decays and annihilations of particles in thermal equilibrium slowly populate the dark sector until the source population becomes Boltzmann suppressed. In the standard freeze-in picture the abundance depends on the decay and annihilation strengths of particles in equilibrium with the baryon-photon fluid, as well as on couplings in the dark sector, and the framework extends beyond the minimal case to dark freeze-out and reannihilation (Bernal et al., 2017).

1. Definition and basic cosmological picture

The defining contrast with weakly interacting massive particles is thermal history. A WIMP begins in thermal equilibrium with the Standard Model bath and freezes out when annihilations become inefficient. A FIMP instead starts with negligible abundance and is gradually produced out of equilibrium; the abundance grows toward a small asymptotic relic value rather than departing from equilibrium (Bernal et al., 2017).

In this framework the decisive mass scale is often not the dark-matter mass itself but the mass scale of the state that feeds the relic abundance through decays or annihilations. One short perspective emphasizes that, for freeze-in, production is usually most effective around the mass scale of a dark partner that sources the dark-matter abundance (Westhoff, 2023). In simple renormalizable realizations, the visible–dark coupling required for freeze-in is typically $y \lesssim \mathcal{O}(10^{-7})$, and in simple decay-driven models it can be around $10^{-12}$ (Bernal et al., 2017).

A recurring misconception is that all FIMP models are merely “under-coupled WIMPs.” The literature instead treats them as a distinct regime: the relic abundance is controlled by source terms from thermal-bath particles, not by the annihilation strength of an equilibrated dark species. This suggests that model-building questions about portal structure, hidden-sector self-interactions, and early-Universe history are not peripheral but intrinsic.

2. Kinetic description and production channels

The microscopic starting point is the Boltzmann equation for the FIMP phase-space distribution,

$$\left( \partial_t - H\,\vec{p}_\chi\cdot \nabla_{p} \right) f_\chi(p_\chi,t) = \sum_j \frac{1}{E_\chi}\int \mathrm{d}C_{\chi,j}\,,$$

with the collision term determined by bath-particle decays and scatterings (Bernal et al., 2017). In the freeze-in regime $f_\chi\ll 1$, inverse processes involving $\chi$ are negligible, so the kinetic equation becomes effectively linear in the bath distributions (D'Eramo et al., 2020).

For the standard decay-driven case $\sigma\to\chi\chi$, the integrated number-density equation is

$$\frac{dn_\chi}{dt} + 3\,H\,n_\chi = 2\,\Gamma_{\sigma\to \chi\chi} \frac{K_1(m_\sigma/T)}{K_2(m_\sigma/T)} n_\sigma^{\rm eq}\,,$$

and the corresponding relic-density estimate is

$$\Omega_{\chi}h^2 \simeq 4.48\times10^{8}\frac{g_\sigma}{g_{*s}\sqrt{g_*}} \frac{m_{\chi}}{{\rm GeV}} \frac{M_{\rm P}\,\Gamma_{\sigma\to \chi\chi}}{m_{\sigma}^2}\,.$$

If $$\Gamma_{\sigma\to \chi\chi}\simeq y^2 m_\sigma/(8\pi)$$, the abundance scales as $y^2$, opposite to freeze-out (Bernal et al., 2017).

Scattering production can be treated analogously. In a generic $10^{-12}$0 channel the reaction density can be written as

$10^{-12}$1

and the yield obeys $10^{-12}$2 (Junius, 2022). For renormalizable interactions the dominant contribution is usually IR-dominated, peaking around the heaviest bath-particle mass in the process, rather than depending on unknown UV physics (D'Eramo et al., 2020).

The phase-space distribution is not a technical afterthought. A model-independent analysis of two-body decays, three-body decays, and binary collisions computes the late-time distribution in terms of a conserved comoving momentum $10^{-12}$3, and shows that two-body decays and $10^{-12}$4 scatterings are warmer than three-body decays (D'Eramo et al., 2020). This difference propagates directly into structure-formation bounds.

3. Portal constructions and theoretical realizations

The review literature organizes FIMP model building around weak portals between the Standard Model and a hidden sector. Canonical examples include the Higgs portal, kinetic mixing, sterile-neutrino frameworks, supersymmetric freeze-in, asymmetric freeze-in, Majoron dark matter, and $10^{-12}$5 extensions such as $10^{-12}$6 and $10^{-12}$7 (Bernal et al., 2017).

A particularly explicit symmetry-motivated realization is “FIMP Dark Matter from Flavon Portals” (Babu et al., 2023). There the dark matter is a Majorana fermion $10^{-12}$8, a spin-$10^{-12}$9, SM-gauge-singlet field carrying a $$\left( \partial_t - H\,\vec{p}_\chi\cdot \nabla_{p} \right) f_\chi(p_\chi,t) = \sum_j \frac{1}{E_\chi}\int \mathrm{d}C_{\chi,j}\,,$$0 flavor charge $$\left( \partial_t - H\,\vec{p}_\chi\cdot \nabla_{p} \right) f_\chi(p_\chi,t) = \sum_j \frac{1}{E_\chi}\int \mathrm{d}C_{\chi,j}\,,$$1, and its mass and couplings arise from Froggatt–Nielsen suppression:

$$\left( \partial_t - H\,\vec{p}_\chi\cdot \nabla_{p} \right) f_\chi(p_\chi,t) = \sum_j \frac{1}{E_\chi}\int \mathrm{d}C_{\chi,j}\,,$$2

With $$\left( \partial_t - H\,\vec{p}_\chi\cdot \nabla_{p} \right) f_\chi(p_\chi,t) = \sum_j \frac{1}{E_\chi}\int \mathrm{d}C_{\chi,j}\,,$$3, large $$\left( \partial_t - H\,\vec{p}_\chi\cdot \nabla_{p} \right) f_\chi(p_\chi,t) = \sum_j \frac{1}{E_\chi}\int \mathrm{d}C_{\chi,j}\,,$$4 automatically yields freeze-in-strength couplings. The same framework also gives a symmetry-based stabilization mechanism: integer charges for Standard Model fields and the flavon, together with a half-integer $$\left( \partial_t - H\,\vec{p}_\chi\cdot \nabla_{p} \right) f_\chi(p_\chi,t) = \sum_j \frac{1}{E_\chi}\int \mathrm{d}C_{\chi,j}\,,$$5 charge for $$\left( \partial_t - H\,\vec{p}_\chi\cdot \nabla_{p} \right) f_\chi(p_\chi,t) = \sum_j \frac{1}{E_\chi}\int \mathrm{d}C_{\chi,j}\,,$$6, forbid operators that would let $$\left( \partial_t - H\,\vec{p}_\chi\cdot \nabla_{p} \right) f_\chi(p_\chi,t) = \sum_j \frac{1}{E_\chi}\int \mathrm{d}C_{\chi,j}\,,$$7 mix with Standard Model neutral fermions or decay (Babu et al., 2023).

Scale invariance yields another distinctive subclass. In “Upgrading Sterile Neutrino Dark Matter to FI$$\left( \partial_t - H\,\vec{p}_\chi\cdot \nabla_{p} \right) f_\chi(p_\chi,t) = \sum_j \frac{1}{E_\chi}\int \mathrm{d}C_{\chi,j}\,,$$8P Using Scale Invariance” (Kang, 2014), the lightest right-handed neutrino $$\left( \partial_t - H\,\vec{p}_\chi\cdot \nabla_{p} \right) f_\chi(p_\chi,t) = \sum_j \frac{1}{E_\chi}\int \mathrm{d}C_{\chi,j}\,,$$9 in a scale-invariant $f_\chi\ll 1$0SISM is produced by singlet-scalar decays, while the same singlet sector generates its mass. The paper emphasizes a 7.1 keV $f_\chi\ll 1$1 with correct relic density in the bulk parameter space. Kang’s “View FImP Miracle (by Scale Invariance) à la Self-interaction” goes further: combining classical scale invariance with freeze-in generically implies an extremely light FIMP, or “FImP,” and for a scalar FImP the lightness naturally accommodates large self-interaction (Kang, 2015).

There are also purely gravitational realizations. In Randall–Sundrum and Clockwork/Linear Dilaton extra dimensions, a scalar FIMP localized on the IR brane can interact with the Standard Model only through the graviton zero mode, Kaluza–Klein gravitons, and radion-like states. In the CW/LD case the observed relic abundance can be reproduced with scalar DM mass in the MeV range and reheating temperatures from $f_\chi\ll 1$2 to $f_\chi\ll 1$3 (Bernal et al., 2020). This suggests that “feeble” need not mean “non-gravitational”; it can also mean “gravitational, but below the thermalization threshold.”

Thermal history around phase transitions can itself become part of the portal physics. In a dark $f_\chi\ll 1$4 model with a massive vector mediator, freeze-in around the phase-transition era requires tracking temperature-dependent masses, first-order transitions, and distinct transverse and longitudinal vector modes; the paper explicitly argues that simple fixed-mass analytic freeze-in estimates are inadequate there (Bian et al., 2021).

4. Nonstandard cosmologies and structure-formation bounds

FIMP production is especially sensitive to the background cosmology because thermal equilibrium never erases early-Universe information. A fast expanding universe with an extra component $f_\chi\ll 1$5 modifies the Hubble rate to

$f_\chi\ll 1$6

and in the leptogenesis-linked sterile-neutrino portal studied in (Chang et al., 2021) this suppresses the final FIMP abundance while enhancing the surviving lepton asymmetry in strong washout. The paper captures the effect with

$f_\chi\ll 1$7

An early matter-dominated era has a related but distinct effect. In the singlet-scalar Higgs-portal example of “From WIMPs to FIMPs: Impact of Early Matter Domination,” freeze-in is weakened both by the larger Hubble rate during production and by later entropy injection, so much larger couplings are required than in radiation domination (Silva-Malpartida et al., 2024). The same paper argues that this can create a continuous and smooth transition between WIMP and FIMP behavior.

Structure formation imposes quantitative lower mass bounds. For renormalizable freeze-in with $f_\chi\ll 1$8 TeV, the model-independent analysis of (D'Eramo et al., 2020) finds the following $f_\chi\ll 1$9-based limits for a FIMP making up all of dark matter:

Production mechanism	Lower bound on $\chi$0	Comment
Two-body decays	$\chi$1 / $\chi$2	conservative / stringent
Three-body decays	$\chi$3 / $\chi$4	colder distribution
Scatterings	$\chi$5 / $\chi$6	close to two-body case

A complementary analytic treatment of small-scale structure derives nonthermal phase-space distributions for Higgs-decay and generic dimension-$\chi$7 scattering production. For Higgs-decay-produced FIMPs it obtains

$\chi$8

for strong (weak) structure constraints, and argues that few-keV FIMPs with suitable self-interactions can address missing satellites, cusp-vs-core, too-big-to-fail, and the diversity problem (Hager et al., 2020).

These results also clarify a second misconception: “freeze-in” does not automatically imply “cold.” Warmness depends on the production channel, the production scale, and the full momentum distribution, not only on the relic density.

5. Experimental access: LLPs, colliders, beam dumps, and indirect signatures

The literature repeatedly treats FIMP testability as difficult but not null. A central theme is that the same tiny couplings that realize freeze-in often imply a long-lived mediator or dark partner. A short perspective on “FIMP Dark Matter at the LHC” states this explicitly and uses axion-like particles as an illustration of the complementarity between ATLAS/CMS, LHCb, Belle II, and FASER (Westhoff, 2023). Sam Junius’s thesis systematizes the point further: if dark matter interacts so weakly with the Standard Model that it never thermalizes, then a heavier connector state often becomes long-lived, and LLP searches at colliders and beam-dump experiments become the experimentally accessible portal to the dark sector (Junius, 2022).

Minimal freeze-in models make the cosmology–collider link particularly transparent. In “Confronting minimal freeze-in models with the LHC,” dark matter is a real scalar singlet $\chi$9 produced mainly by the decay of a vector-like parent $\sigma\to\chi\chi$0, and the relic-density condition implies a characteristic scaling

$\sigma\to\chi\chi$1

up to reheating-temperature and $\sigma\to\chi\chi$2 factors (Bélanger et al., 2019). Because $\sigma\to\chi\chi$3 is gauge charged, the same feeble coupling that fixes the freeze-in yield also makes $\sigma\to\chi\chi$4 an LLP, leading to heavy stable charged-particle searches, disappearing tracks, displaced leptons, and displaced vertices plus missing transverse energy.

Prompt missing-energy signatures can also arise. In a gluophilic $\sigma\to\chi\chi$5 portal, the dominant early-Universe process is

$\sigma\to\chi\chi$6

with a reaction density scaling as $\sigma\to\chi\chi$7, so freeze-in is reheating-dominated. The same portal yields monojet $\sigma\to\chi\chi$8 signatures at the LHC, and the paper concludes that a large region of parameter space, for FIMP masses between the MeV scale and the collider threshold of $\sigma\to\chi\chi$9 TeV, is already excluded by monojet limits (Claude et al., 2022).

Indirect signals become more promising in multicomponent setups. “Probing multicomponent FIMP scenarios with gamma-ray telescopes” studies two-FIMP sectors in which the heavier frozen-in state decays to the lighter one through loop-induced channels such as

$$\frac{dn_\chi}{dt} + 3\,H\,n_\chi = 2\,\Gamma_{\sigma\to \chi\chi} \frac{K_1(m_\sigma/T)}{K_2(m_\sigma/T)} n_\sigma^{\rm eq}\,,$$0

and argues that the resulting sharp gamma-ray features can be detectable for parameter values compatible with the observed dark-matter abundance (Herms et al., 2019). This is an important qualification to the common statement that FIMPs are invisible in indirect detection.

6. Conceptual issues, refinements, and open directions

Several technical issues recur across the literature. First, the minimal freeze-in estimate is not always the end of the story. The review emphasizes that hidden-sector self-interactions can thermalize the dark sector internally, leading to dark freeze-out, cannibalization, or reannihilation instead of a purely source-dominated relic (Bernal et al., 2017). This suggests that “freeze-in” is often only the first stage of a more elaborate hidden-sector evolution.

Second, primordial and UV sensitivity are genuine parts of the subject. Because FIMPs never thermalize with the Standard Model, initial conditions can matter. The review accordingly highlights reheating dependence, higher-dimensional operators, and inflationary spectator-field fluctuations, and derives an isocurvature lower bound on a scalar self-coupling,

$$\frac{dn_\chi}{dt} + 3\,H\,n_\chi = 2\,\Gamma_{\sigma\to \chi\chi} \frac{K_1(m_\sigma/T)}{K_2(m_\sigma/T)} n_\sigma^{\rm eq}\,,$$1

as one example of a cosmological constraint that has no WIMP analogue (Bernal et al., 2017).

Third, phase-transition-era production can invalidate fixed-mass intuition. In the dark $$\frac{dn_\chi}{dt} + 3\,H\,n_\chi = 2\,\Gamma_{\sigma\to \chi\chi} \frac{K_1(m_\sigma/T)}{K_2(m_\sigma/T)} n_\sigma^{\rm eq}\,,$$2 study already noted, the dominant freeze-in channel can switch several times as temperature changes, first-order transitions can produce discontinuous jumps in the reaction density, and the distinct thermal dispersion relations of transverse and longitudinal vector modes materially affect the relic-density calculation (Bian et al., 2021). A plausible implication is that fully thermal, phase-aware treatments are indispensable whenever production occurs near symmetry-breaking scales.

Taken together, these works define FIMPs not as a single model but as a broad class of nonthermal dark-matter scenarios in which the relic abundance is set by feeble source terms rather than by annihilation from equilibrium. Within that class, the main discriminants are the portal structure, hidden-sector dynamics, early-Universe background, and the momentum distribution imprinted during production. The resulting phenomenology spans keV warm-like relics, MeV purely gravitational dark matter, GeV–TeV LLP mediators, and symmetry-based constructions in which the same dynamics explain flavor, scale generation, or self-interaction as well as freeze-in.