Dark Dimension Proposal

• The dark dimension proposal is a framework integrating quantum gravity, string theory, and cosmology to explain dark energy scales via a micron-sized extra spatial dimension.
• String theory constructions like warped throats and T-fold reductions naturally realize the Kaluza-Klein spectrum and set key mass hierarchies within the model.
• The proposal unifies dark matter and dark energy by linking KK gravitons, axionic fields, and neutrino phenomenology, offering clear experimental predictions.

The dark dimension proposal is a framework at the intersection of quantum gravity, string theory, and cosmological observations that posits the existence of a single extra spatial dimension of mesoscopic (micron) size. This extra dimension emerges as a natural consequence of combining Swampland conjectures about the limits of consistent low-energy effective field theories with the observed smallness of dark energy. The resulting setup predicts a close relationship between the cosmological constant, observable mass hierarchies, dark matter, and new cosmological phenomena, fundamentally altering our understanding of the dark sector and potentially leading to distinctive experimental signatures.

1. Origin of the Dark Dimension: Swampland and Hierarchy Principles

The dark dimension arises from the Swampland program, which aims to distinguish effective field theories that can be UV-completed into quantum gravity (the "landscape") from those that cannot (the "swampland"). A central tenet is the Distance Conjecture, which posits that as one approaches an infinite distance in moduli space (e.g., the limit where the four-dimensional cosmological constant $\Lambda$ vanishes), a tower of states becomes light, with masses scaling as $m \sim |\Lambda|^\alpha$, where $\alpha$ is constrained by theoretical and phenomenological considerations. Analyses combining the Swampland conjectures with observational data (e.g., the measured value $\Lambda \simeq 10^{-122} M_\text{pl}^4$) single out $\alpha = 1/4$ as compatible with astrophysical and experimental bounds (Anchordoqui, 2022, Blumenhagen et al., 2022, Anchordoqui et al., 7 May 2024).

This scaling implies a unique regime where the radius $R$ of a single extra spatial dimension is set by

$R \sim \lambda \Lambda^{-1/4} \,,$

where the order-unity parameter $0.0001 \lesssim \lambda \lesssim 0.1$ is determined by flux quantization and other string-theoretic factors (Noble et al., 2023, Fadafan et al., 2023). Numerically, this places $R$ in the range of one to tens of microns, far larger than conventional compactification scales. Higher-dimensional Planck and species scales, as well as the Kaluza-Klein (KK) gap for graviton excitations, are then set consistently by this geometric framework (Gonzalo et al., 2022, Fadafan et al., 2023).

2. String Theory Realizations and Geometric Mechanisms

Explicit string and M-theory compactifications provide concrete settings for this framework:

• Warped Throat Constructions: Warped throats (e.g., Klebanov–Strassler geometries) naturally realize the scaling $m_\text{KK} \sim \Lambda^{1/4}$, as deep redshifts of KK towers in warped regions set the required low-energy scales. The value of $\lambda$ is determined by combinations of flux numbers and geometric parameters (e.g., $g_s$, $M$, $y_\text{UV}$) (Blumenhagen et al., 2022).
• T-fold and Scherk–Schwarz Reductions: Non-geometric compactifications (T-folds) with duality twists stabilize moduli so that a single runaway direction—the Scherk–Schwarz radion—remains, with its vacuum expectation value dynamically setting the dark dimension scale and the exponential potential governing its evolution. The scalar potential scales as $V \propto m_\text{KK}^4$ (Nian et al., 28 Nov 2024).
• Brane Localizations and Topology: The Standard Model is localized on a 3-brane, while gravity, axions, and possibly right-handed neutrinos propagate in the bulk. The topology of the dark dimension may be a circle (with the SM brane localized in a small region) or an interval (with two "end-of-the-world" branes, one possibly containing parallel hidden sectors) (Schwarz, 19 Mar 2024, Anchordoqui et al., 7 May 2024).

This geometry robustly ties $\Lambda$ to the KK gap and allows all relevant mass hierarchies (Planck, QCD axion, neutrinos, EW scale) to emerge from purely geometric considerations (Fadafan et al., 2023, Vafa, 1 Feb 2024).

3. Dark Matter and Cosmological Phenomenology

A distinctive feature of the proposal is the unification of dark matter and dark energy through the physics of the dark dimension:

• KK Gravitons as Dark Matter: The universal coupling of brane-localized Standard Model fields to bulk gravitons means that the KK tower associated with the dark dimension provides a natural and unavoidable candidate for dark matter. Production occurs via gravitational freeze-in at temperatures set by the dark energy scale ($T_i \sim 4\,\mathrm{GeV}$), with subsequent intra-tower decays cascading the dominant mass mode down to $m_\text{DM} \sim 1$--100\,keV today (Gonzalo et al., 2022), ensuring lifetimes long compared to the age of the universe.
• Cosmological Coincidence Problem: The observed overlap between matter–radiation equality temperature ($T \sim 1\,\mathrm{eV}$) and the onset of dark energy domination emerges as a dynamical outcome. The cosmological yield of KK graviton dark matter directly matches the timing when the dark energy becomes important, eliminating the need for anthropic explanations (Gonzalo et al., 2022, Vafa, 1 Feb 2024).
• Axion and Ultralight Dark Matter: Brane-localized axions have their decay constant $f_a$ bounded from above by the 5d Planck mass ($f_a \lesssim 10^{9}$--$10^{10}$ GeV), leading to a narrow axion mass window ($m_a \sim 10^{-3}$--$10^{-2}$ eV) (Li, 27 Dec 2024). A two-axion mixing mechanism (e.g., with an ALP possessing $m_A \sim 10^{-5}$ eV, $f_A \sim 10^{11}$ GeV) allows the QCD axion to comprise all of DM via resonant conversion, otherwise only a minor fraction of the total (Li, 27 Dec 2024).
• Neutrino Sector: Right-handed neutrinos propagating in the bulk ("dark dimension right-handed neutrinos") generate naturally suppressed Dirac neutrino masses ($m_\nu \sim \langle H \rangle / \sqrt{R M_*}$), while their KK excitation spectrum produces distinctive signatures—multiple kinks or a single effective kink — in the tritium $\beta$-decay spectrum accessible to the KATRIN experiment (Antoniadis et al., 5 Sep 2025, Anchordoqui et al., 7 May 2024).

4. Evolution of the Dark Sector and Experimental Implications

The scalar modulus controlling the dark dimension ($\phi$) is expected to roll, driving an evolving dark energy and correlated variation in the dark matter mass scale: $$V(\phi) = V_0 e^{-c\phi} \,, \quad m_\text{DM}(\phi) = m_0 e^{-c'\phi} \,.$$ Parameters $c, c'$ are generically $\mathcal{O}(1)$ in Planck units, but cosmological fits (e.g., to DESI DR2, Pantheon+) yield $c' \simeq 0.05 \pm 0.01$ (Bedroya et al., 3 Jul 2025). This correlation gives a physical realization of effective phantom behavior ($w_\text{eff} < -1$) naturally, matching observational data as well as standard parametrizations but with added theoretical motivation.

Experimental probes are imminent:

Observable	Predicted Signature	Typical Parameter Range
Short-range gravity	Deviations in $1/r$ law at $R \sim 1$--$10\,\mu$m	$\lambda \lesssim 10^{-3}$
UHECR spectra	Universal cutoff at $E_\mathrm{UV} \sim 10^{10.6}$ GeV	$M_\text{UV} \sim 10^{10}$ GeV
KATRIN/Kalorimeters	Multiple spectral kinks from KK right-handed neutrinos	$R \sim 1$--$10\,\mu$m
PTA, DM haloes	Fluctuations in gravitational potential, FDM pressure	$m \sim 10^{-23}$–$10^{-22}$ eV
$\gamma$-Ray, PBH	Modification of evaporation, allowed PBH DM mass window	$$10^{11} \lesssim M_\text{PBH}/\mathrm{g} \lesssim 10^{21}$$

The KK graviton dark matter, axion parameter space, and neutrino mass relations are all subject to ongoing and next-generation experimental scrutiny (Noble et al., 2023, Antoniadis et al., 5 Sep 2025). Torsion-balance experiments and atom interferometry probe gravity at micron distances (Schwarz, 19 Mar 2024). UHECR observatories (Auger, TA) test universal cutoff predictions in the presence of a dark dimension (Noble et al., 2023).

5. Phenomenological Challenges and Model Consistency

String-theoretic realizations encounter important constraints:

• KK Towers and Moduli Stabilization: Ensuring only one extra dimension remains light (with all other moduli stabilized at sufficiently high masses) is challenging, especially in warped throat and large volume compactifications (Blumenhagen et al., 2022, Anchordoqui et al., 7 May 2024). The tuning of fluxes and moduli must avoid conflict with astrophysical and gravitational tests.
• Gravity and Standard Model Hierarchies: The warped double-throat scenario enables the emergence of both the Planck and electroweak scales from just two geometric inputs ($10^{-2}$ eV and $10^{10}$ GeV), offering solutions to the hierarchy and naturalness problems (Fadafan et al., 2023).
• Low-Energy Model Building: The suppression of quantum contributions to $\Lambda$ and localized warping is used to absorb large brane tensions arising from the SM sector without destabilizing the small effective 4D cosmological constant (Fadafan et al., 2023, Anchordoqui et al., 7 May 2024).

6. Outlook and Theoretical Impact

The dark dimension scenario forms a unique, predictive corner of the quantum gravity landscape, correlating:

• The tiny observed $\Lambda$ with the existence of a single mesoscopic dimension,
• Emergence of the KK graviton (or other bulk excitations) as dark matter,
• A solution to the cosmological coincidence and "why now" problems,
• Predictive mass windows for QCD axions, sterile neutrinos, and possible signatures in KATRIN and gravitational experiments,
• Potential unification of the dark sector emerged from string and M-theory principles (Blumenhagen et al., 2022, Fadafan et al., 2023, Schwarz, 19 Mar 2024, Bedroya et al., 3 Jul 2025).

Future experimental tests at the interface of cosmology, particle physics, and gravitational phenomenology are poised to probe core predictions — possibly lending support to or falsifying the presence of a dark dimension as a cornerstone of ultraviolet-complete theories describing our universe.