Graviton-Portal Dark Matter

• Graviton-portal dark matter refers to models where dark matter interacts with the Standard Model exclusively through gravitational sectors, using mediators beyond the massless graviton.
• These frameworks employ various mechanisms—including massive spin-2 exchange, curvature-induced couplings, and torsion portals—to produce dark matter nonthermally via freeze-in or, in some cases, thermal freeze-out.
• Phenomenological studies address production rates, decay stability, and collider signals, emphasizing UV sensitivity, gauge cancellations, and distinct constraints for different dark matter spins.

Graviton-portal dark matter denotes a family of scenarios in which dark matter communicates with the Standard Model through the gravitational sector rather than through ordinary renormalizable portals. In the literature, this family includes direct coupling to the massless graviton, exchange of an additional massive spin-2 field, contact interactions built from energy-momentum tensors, curvature-induced portals, torsion-induced portals in Einstein–Cartan gravity, extra-dimensional Kaluza–Klein gravitons, and even models in which the dark component is itself a graviton-sector degree of freedom (Bernal et al., 2018, Anastasopoulos et al., 2020, Shaposhnikov et al., 2020, Pirogov, 2014).

1. Operator content and mediator taxonomy

The narrowest realization is a genuinely spin-2 portal. A representative formulation contains the ordinary graviton $h_{\mu\nu}$ and an additional massive spin-2 mediator $\tilde h_{\mu\nu}$, with interaction terms

$${\cal L}_{\rm int}^1 = \frac{1}{2M_P}\, h_{\mu\nu}\left(T_{\rm SM}^{\mu\nu}+T_X^{\mu\nu}\right),\qquad {\cal L}_{\rm int}^2 = \frac{1}{\Lambda}\, \tilde h_{\mu\nu}\left(T_{\rm SM}^{\mu\nu}+T_X^{\mu\nu}\right),$$

so that the portal remains universal in tensor structure but is no longer fixed to Planck suppression (Bernal et al., 2018). Closely related effective descriptions replace explicit mediator exchange by a dimension-8 tensor contact operator,

$${\cal L}_{\rm portal} = -\frac{1}{2\Lambda^4}T^{\mu\nu}_{\rm SM}T_{\mu\nu}^{\rm hidden},$$

which may arise from emergent gravity, heavy spin-2 exchange, or other UV completions (Anastasopoulos et al., 2020).

A broader usage of the term includes curvature-induced portals. In scalar dark-matter models, the defining operator can be a nonminimal linear coupling to the Ricci scalar,

$\mathcal{L}_\xi=-\xi M R \phi,$

or, more generally, $-\xi R f(\varphi,X)$, with $f$ linear in the dark field (Bezrukov et al., 2020, Catà et al., 2016). After Weyl transformation to Einstein frame, such operators generate an infinite tower of Planck-suppressed couplings between one dark-matter field and Standard Model Higgs, Yukawa, and derivative structures. This construction is gravitationally induced, but it is not identical to ordinary graviton exchange.

Einstein–Cartan gravity provides a different portal mechanism. There the mediator is not primarily a propagating spin-2 excitation but the non-propagating torsion components of the spin connection. Eliminating torsion generates local four-fermion and scalar-fermion operators, including

$$L_{4f}= \dfrac{3\alpha^2}{16 M_P^2} V^\mu V_\mu + \dfrac{3 \alpha \beta}{8M_P^2} V^\mu A_\mu -\dfrac{3-3\beta^2}{16M_P^2} A^\mu A_\mu ,$$

which couple Standard Model fermion currents to a singlet fermion $N$ (Shaposhnikov et al., 2020). In that sense, some “gravitational portals” are torsion portals rather than graviton portals in the strict spin-2 sense.

A still broader limit is realized in graviton-sector dark matter. In Unimodular Bimode Gravity, the additional scalar degree of freedom

$\sigma \equiv \ln \frac{\sqrt{-g}}{\bar\mu}$

is treated as an “(almost) massless scalar graviton” and identified with gravitational dark matter (Pirogov, 2014). Here the dark sector is not coupled to gravity; it is part of gravity.

2. Production in the early Universe

A central theme of graviton-portal dark matter is nonthermal production, especially freeze-in. In the generic spin-2 portal with both $\tilde h_{\mu\nu}$0 and $\tilde h_{\mu\nu}$1, production during reheating falls into four regimes: graviton-dominated production with $\tilde h_{\mu\nu}$2; light-mediator production with $\tilde h_{\mu\nu}$3; resonant production when $\tilde h_{\mu\nu}$4; and heavy-mediator production with $\tilde h_{\mu\nu}$5 (Bernal et al., 2018). The heavy-mediator regime is strongly UV dominated, and the paper emphasizes that the maximum reheating temperature $\tilde h_{\mu\nu}$6, not only the final reheating temperature $\tilde h_{\mu\nu}$7, can dominate the abundance.

The energy-momentum portal displays the same UV character in a particularly transparent form. Summing over relativistic Standard Model species gives

$\tilde h_{\mu\nu}$8

with $\tilde h_{\mu\nu}$9, $${\cal L}_{\rm int}^1 = \frac{1}{2M_P}\, h_{\mu\nu}\left(T_{\rm SM}^{\mu\nu}+T_X^{\mu\nu}\right),\qquad {\cal L}_{\rm int}^2 = \frac{1}{\Lambda}\, \tilde h_{\mu\nu}\left(T_{\rm SM}^{\mu\nu}+T_X^{\mu\nu}\right),$$0, and $${\cal L}_{\rm int}^1 = \frac{1}{2M_P}\, h_{\mu\nu}\left(T_{\rm SM}^{\mu\nu}+T_X^{\mu\nu}\right),\qquad {\cal L}_{\rm int}^2 = \frac{1}{\Lambda}\, \tilde h_{\mu\nu}\left(T_{\rm SM}^{\mu\nu}+T_X^{\mu\nu}\right),$$1 for scalar, fermion, and vector dark matter, respectively (Anastasopoulos et al., 2020). The corresponding relic density from bath scattering scales as

$${\cal L}_{\rm int}^1 = \frac{1}{2M_P}\, h_{\mu\nu}\left(T_{\rm SM}^{\mu\nu}+T_X^{\mu\nu}\right),\qquad {\cal L}_{\rm int}^2 = \frac{1}{\Lambda}\, \tilde h_{\mu\nu}\left(T_{\rm SM}^{\mu\nu}+T_X^{\mu\nu}\right),$$2

which is the characteristic dimension-8 UV-freeze-in behavior.

Einstein–Cartan production is also freeze-in, but the portal operator is torsion-induced and fermionic. The dominant process is

$${\cal L}_{\rm int}^1 = \frac{1}{2M_P}\, h_{\mu\nu}\left(T_{\rm SM}^{\mu\nu}+T_X^{\mu\nu}\right),\qquad {\cal L}_{\rm int}^2 = \frac{1}{\Lambda}\, \tilde h_{\mu\nu}\left(T_{\rm SM}^{\mu\nu}+T_X^{\mu\nu}\right),$$3

with $${\cal L}_{\rm int}^1 = \frac{1}{2M_P}\, h_{\mu\nu}\left(T_{\rm SM}^{\mu\nu}+T_X^{\mu\nu}\right),\qquad {\cal L}_{\rm int}^2 = \frac{1}{\Lambda}\, \tilde h_{\mu\nu}\left(T_{\rm SM}^{\mu\nu}+T_X^{\mu\nu}\right),$$4 any Standard Model fermion. The rate takes the form

$${\cal L}_{\rm int}^1 = \frac{1}{2M_P}\, h_{\mu\nu}\left(T_{\rm SM}^{\mu\nu}+T_X^{\mu\nu}\right),\qquad {\cal L}_{\rm int}^2 = \frac{1}{\Lambda}\, \tilde h_{\mu\nu}\left(T_{\rm SM}^{\mu\nu}+T_X^{\mu\nu}\right),$$5

and the mechanism is operative for singlet-fermion dark matter masses “from a few keV up to $${\cal L}_{\rm int}^1 = \frac{1}{2M_P}\, h_{\mu\nu}\left(T_{\rm SM}^{\mu\nu}+T_X^{\mu\nu}\right),\qquad {\cal L}_{\rm int}^2 = \frac{1}{\Lambda}\, \tilde h_{\mu\nu}\left(T_{\rm SM}^{\mu\nu}+T_X^{\mu\nu}\right),$$6 GeV” (Shaposhnikov et al., 2020). In the Palatini Higgs-inflation benchmark used there, $${\cal L}_{\rm int}^1 = \frac{1}{2M_P}\, h_{\mu\nu}\left(T_{\rm SM}^{\mu\nu}+T_X^{\mu\nu}\right),\qquad {\cal L}_{\rm int}^2 = \frac{1}{\Lambda}\, \tilde h_{\mu\nu}\left(T_{\rm SM}^{\mu\nu}+T_X^{\mu\nu}\right),$$7, yielding either very heavy dark matter in the minimal-coupling regime or keV-scale warm dark matter when $${\cal L}_{\rm int}^1 = \frac{1}{2M_P}\, h_{\mu\nu}\left(T_{\rm SM}^{\mu\nu}+T_X^{\mu\nu}\right),\qquad {\cal L}_{\rm int}^2 = \frac{1}{\Lambda}\, \tilde h_{\mu\nu}\left(T_{\rm SM}^{\mu\nu}+T_X^{\mu\nu}\right),$$8 (Shaposhnikov et al., 2020).

A more unified construction uses gravity as the sole connector between the inflaton, the Standard Model, and right-handed neutrinos. With non-minimal gravitational couplings, the viable region singled out by that analysis has $${\cal L}_{\rm int}^1 = \frac{1}{2M_P}\, h_{\mu\nu}\left(T_{\rm SM}^{\mu\nu}+T_X^{\mu\nu}\right),\qquad {\cal L}_{\rm int}^2 = \frac{1}{\Lambda}\, \tilde h_{\mu\nu}\left(T_{\rm SM}^{\mu\nu}+T_X^{\mu\nu}\right),$$9 PeV for the dark-matter state, $${\cal L}_{\rm portal} = -\frac{1}{2\Lambda^4}T^{\mu\nu}_{\rm SM}T_{\mu\nu}^{\rm hidden},$$0 GeV for the leptogenesis state, and $${\cal L}_{\rm portal} = -\frac{1}{2\Lambda^4}T^{\mu\nu}_{\rm SM}T_{\mu\nu}^{\rm hidden},$$1 GeV for $${\cal L}_{\rm portal} = -\frac{1}{2\Lambda^4}T^{\mu\nu}_{\rm SM}T_{\mu\nu}^{\rm hidden},$$2 (Barman et al., 2022). The same paper also proposes a two-step mechanism in which gravity first produces scalars that later decay into fermionic dark matter, removing the helicity suppression of direct fermion production (Barman et al., 2022).

3. Decay, stability, and gravitational symmetry breaking

The decay problem is fundamental for gravity portals because global symmetries that stabilize dark matter in flat spacetime need not survive nonminimal couplings to curvature. A systematic study of curvature-induced decay considered three benchmarks: a real scalar singlet, an inert scalar doublet, and a fermionic singlet (Catà et al., 2016). The central conclusion was asymmetric. The scalar singlet is severely constrained, while the scalar doublet and fermionic singlet are much better protected, the former by gauge symmetry and the latter by Lorentz symmetry (Catà et al., 2016).

For the scalar singlet, the dangerous operator is linear and dimension three, $${\cal L}_{\rm portal} = -\frac{1}{2\Lambda^4}T^{\mu\nu}_{\rm SM}T_{\mu\nu}^{\rm hidden},$$3, so the induced Einstein-frame interaction directly couples one dark-matter field to Higgs kinetic terms, Yukawas, and the Higgs potential (Catà et al., 2016). The paper finds that the resulting limits are “remarkably strong and exclude large regions of the parameter space,” implying that an additional stabilizing symmetry is generally required (Catà et al., 2016). In contrast, the inert-doublet operator must appear as $${\cal L}_{\rm portal} = -\frac{1}{2\Lambda^4}T^{\mu\nu}_{\rm SM}T_{\mu\nu}^{\rm hidden},$$4, and the fermionic singlet requires a dimension-6 structure $${\cal L}_{\rm portal} = -\frac{1}{2\Lambda^4}T^{\mu\nu}_{\rm SM}T_{\mu\nu}^{\rm hidden},$$5, so their decay widths are much more suppressed.

The quantitative headline is that for a nonminimal coupling parameter $${\cal L}_{\rm portal} = -\frac{1}{2\Lambda^4}T^{\mu\nu}_{\rm SM}T_{\mu\nu}^{\rm hidden},$$6, decays through the gravity portal remain compatible with observations if the dark-matter mass is smaller than $${\cal L}_{\rm portal} = -\frac{1}{2\Lambda^4}T^{\mu\nu}_{\rm SM}T_{\mu\nu}^{\rm hidden},$$7 GeV for the scalar doublet and $${\cal L}_{\rm portal} = -\frac{1}{2\Lambda^4}T^{\mu\nu}_{\rm SM}T_{\mu\nu}^{\rm hidden},$$8 GeV for the fermionic singlet (Catà et al., 2016). Multi-body final states involving longitudinal $${\cal L}_{\rm portal} = -\frac{1}{2\Lambda^4}T^{\mu\nu}_{\rm SM}T_{\mu\nu}^{\rm hidden},$$9, $\mathcal{L}_\xi=-\xi M R \phi,$0, and Higgs bosons dominate the high-mass regime, so gravitational decay phenomenology is not generically two-body.

A later correction substantially changed the interpretation of heavy scalar-curvature portals. Earlier literature had claimed a dramatic growth of decay amplitudes with dark-matter mass due to longitudinal electroweak bosons, but the reanalysis showed that the leading longitudinal pieces cancel exactly in the full tree-level amplitudes (Bezrukov et al., 2020). The corrected result is that perturbative widths are controlled by the strong-coupling scale

$\mathcal{L}_\xi=-\xi M R \phi,$1

and scale generically as

$\mathcal{L}_\xi=-\xi M R \phi,$2

without any “miraculous” enhancement by powers of $\mathcal{L}_\xi=-\xi M R \phi,$3 (Bezrukov et al., 2020). This correction markedly lengthens the expected lifetime and weakens indirect-detection expectations in scalar-curvature portal models.

4. Spin-2 portal phenomenology at the TeV scale

Once the mediator is a genuine massive spin-2 state rather than a pure Planck-suppressed graviton, thermal freeze-out becomes possible. In ghost-free bi-gravity, the spectrum contains both the usual massless graviton $\mathcal{L}_\xi=-\xi M R \phi,$4 and a massive spin-2 field $\mathcal{L}_\xi=-\xi M R \phi,$5, with Standard Model and dark matter coupled through different composite metrics (Chen et al., 2023). The massless contribution to direct detection is negligible, while the massive spin-2 can mediate both dark-matter–nucleon scattering and dark-matter self-interactions.

The direct-detection cross section in that construction is controlled by

$\mathcal{L}_\xi=-\xi M R \phi,$6

while the self-interaction potential is Yukawa-like,

$\mathcal{L}_\xi=-\xi M R \phi,$7

The phenomenologically emphasized region is $\mathcal{L}_\xi=-\xi M R \phi,$8 and $\mathcal{L}_\xi=-\xi M R \phi,$9, with a reheating temperature of order $-\xi R f(\varphi,X)$0 GeV from freeze-in (Chen et al., 2023).

Radius-stabilized Randall–Sundrum models provide a more tightly constrained KK-graviton portal. In the light-radion, weak-backreaction regime, the portal is mediated mainly by massive spin-2 KK gravitons, while the radion is subdominant for annihilation but can dominate direct detection because the spin-independent cross section scales as $-\xi R f(\varphi,X)$1 (Chivukula et al., 2024). A key technical result is that amplitudes involving massive spin-2 KK states exhibit nontrivial cancellations; after those are included, nonresonant annihilation is much weaker than naive power counting would suggest (Chivukula et al., 2024).

The thermal-freeze-out consequence is that viable KK-graviton portals are resonant. Scalar dark matter is “essentially ruled out” in the standard thermal freeze-out scenario, whereas vector dark matter is viable for masses ranging from $-\xi R f(\varphi,X)$2 TeV to $-\xi R f(\varphi,X)$3 TeV for coupling scales of order $-\xi R f(\varphi,X)$4 TeV or lower, and fermion dark matter is viable in a similar mass range only for KK coupling scales of order $-\xi R f(\varphi,X)$5 TeV (Chivukula et al., 2024). This makes the dependence on dark-matter spin a structural feature of spin-2 freeze-out models rather than a minor model-building choice.

5. Extra-dimensional and graviton-sector realizations

Extra dimensions furnish several of the most concrete graviton-portal constructions. In a six-dimensional nested-warped embedding of Universal Extra Dimensions, the dominant mediator is the first graviton excitation along the warped direction, $-\xi R f(\varphi,X)$6, and the central resonance is

$-\xi R f(\varphi,X)$7

This graviton portal opens additional annihilation channels and allows $-\xi R f(\varphi,X)$8 up to roughly $-\xi R f(\varphi,X)$9, alleviating the relic-density/LHC tension of minimal UED (Arun et al., 2017). The most distinctive indirect-detection signature is a potentially sizable $f$0 line near resonance (Arun et al., 2017).

A different extra-dimensional realization appears in the Dark Dimension proposal, where the dark matter is the tower of massive spin-2 KK excitations of the graviton itself (Gonzalo et al., 2022). In that scenario, the Standard Model is localized on a brane and the bulk graviton universally couples to the brane stress tensor, so KK gravitons are produced gravitationally at $f$1 GeV (Gonzalo et al., 2022). The initially heavier modes cascade dominantly into lighter KK gravitons; the present-day dark-matter mass is estimated to be $f$2 keV, and the total fraction of energy lost in decays is reported to be less than $f$3 (Gonzalo et al., 2022). This is not a portal to a hidden matter field; it is a portal to a graviton tower that becomes the dark matter.

At the opposite conceptual extreme lies Unimodular Bimode Gravity, in which the dark component is a scalar graviton or “systolon” with action

$f$4

Its spherically symmetric vacuum solution yields soft-core halos with asymptotically flat rotation curves, and the asymptotic circular speed is

$f$5

for galactic applications (Pirogov, 2014). This realization suggests that “graviton-portal dark matter” can also denote theories where the portal and the dark sector are unified inside the gravitational field content itself.

6. Consistency conditions, misconceptions, and unresolved issues

A recurring misconception is that any gravity portal automatically reduces to massless graviton exchange. The literature does not support that identification. Einstein–Cartan models are torsion-mediated in the low-energy theory; energy-momentum portals are local tensor operators after integrating out a heavy mediator; KK-graviton models rely on massive spin-2 resonances; and graviton-sector dark matter dispenses with a separate hidden matter field altogether (Shaposhnikov et al., 2020, Anastasopoulos et al., 2020, Arun et al., 2017). The phrase therefore functions as a structural label for gravity-dominated communication, not a unique Lagrangian template.

A second misconception concerns amplitude growth. The scalar-curvature portal literature originally claimed pronounced enhancement from longitudinal electroweak bosons, but the corrected analysis showed that gauge-invariant cancellations eliminate those terms (Bezrukov et al., 2020). An analogous issue reappears in KK-graviton portals, where consistent higher-dimensional couplings enforce cancellations among contact, spin-2, and scalar diagrams (Chivukula et al., 2024). In both contexts, naive power counting overestimates rates unless the full gauge- and gravity-consistent amplitude is retained.

Effective-field-theory consistency also imposes nontrivial positivity constraints. In a derivative Higgs-portal EFT motivated by massive graviton, radion, and general metric couplings, the dimension-8 coefficients obey

$f$6

together with mixed inequalities involving Higgs and dark-matter self-interactions (Kim et al., 2023). Massive graviton and radion completions were found to respect these bounds, whereas disformal metric couplings can allow subluminal propagation of the graviton but violate positivity (Kim et al., 2023). This does not exclude every metric-mediated portal, but it sharply narrows the class of EFTs with standard analytic UV completion.

Finally, many results remain strongly cosmology dependent. UV freeze-in through tensor portals scales with $f$7 or $f$8, and in several cases the abundance is dominated by the highest post-inflationary temperatures rather than by late thermal history (Bernal et al., 2018, Anastasopoulos et al., 2020). Some scenarios also retain model-specific caveats: the dark-dimension graviton analysis does not provide a full free-streaming or Lyman-$f$9 treatment, and the radius-stabilized Randall–Sundrum study explicitly restricts itself to the light-radion, weak-backreaction regime, leaving heavy-radion phenomenology to future work (Gonzalo et al., 2022, Chivukula et al., 2024). This suggests that the most robust statements in the subject are structural—universal stress-tensor couplings, reheating sensitivity, spin dependence, and the importance of exact amplitude cancellations—while detailed viability remains highly UV and cosmology dependent.