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dark matter

1. Observational Evidence

Dark matter was first suggested by Fritz Zwicky (1933) from galaxy cluster dynamics, and later confirmed by many observations:

  • Galaxy rotation curves: stars orbit too fast for visible matter alone.
  • Gravitational lensing: mass inferred from bending of light exceeds luminous matter.
  • Cosmic Microwave Background (CMB): anisotropies measured by Planck imply ΩDM≈0.26\Omega_{\text{DM}} \approx 0.26.
  • Large-Scale Structure: growth of galaxies and clusters requires unseen mass.

Rotation Curves

For a star at radius rr, orbital velocity:

v(r)=GM(r)r.v(r) = \sqrt{\frac{G M(r)}{r}}.

Observed: v(r)≈constv(r) \approx \text{const} for large rr.
Expected from visible matter: v(r)∼1/rv(r) \sim 1/\sqrt{r}.
⇒ Requires dark halo.

2. Cosmological Parameters

From Λ\LambdaCDM fits to Planck data:

  • Total: Ωtot≃1.0\Omega_{\text{tot}} \simeq 1.0 (flat universe)
  • Dark Energy: ΩΛ≃0.69\Omega_\Lambda \simeq 0.69
  • Dark Matter: ΩDM≃0.26\Omega_{\text{DM}} \simeq 0.26
  • Baryons: Ωb≃0.05\Omega_b \simeq 0.05

Thus, dark matter dominates over baryonic matter by about 5:1.

3. Candidate Particles

(a) WIMPs (Weakly Interacting Massive Particles)

  • Mass range: 10 GeV≲m≲10 TeV10 \,\text{GeV} \lesssim m \lesssim 10 \,\text{TeV}
  • Relic density set by thermal freeze-out:
ΩDMh2≈3×10−27 cm3/s⟨σv⟩.\Omega_{\text{DM}} h^2 \approx \frac{3 \times 10^{-27} \,\text{cm}^3/\text{s}}{\langle \sigma v \rangle}.

The “WIMP miracle”: electroweak-scale cross sections naturally yield the observed density.

(b) Axions

  • Arise from Peccei–Quinn solution to the strong CP problem.
  • Very light (μeV\mu\text{eV}–meV\text{meV}), but produced non-thermally.
  • Coupling to photons:
Laγγ=gaγγa E⋅B.\mathcal{L}_{a\gamma\gamma} = g_{a\gamma\gamma} a \, \mathbf{E}\cdot \mathbf{B}.

(c) Sterile Neutrinos

  • Right-handed neutrinos with keV masses.
  • Warm dark matter candidate.

(d) Other proposals

  • Self-interacting DM, dark sectors, primordial black holes.

4. Detection Strategies

  1. Direct detection

    • Look for nuclear recoils from DM scattering.
    • Experiments: XENONnT, LUX-ZEPLIN (LZ), PandaX.
    • Signal rate:
    R∝ρχmχ⟨σχNv⟩.R \propto \frac{\rho_{\chi}}{m_\chi} \langle \sigma_{\chi N} v \rangle.

  2. Indirect detection

    • Search for annihilation/decay products: γ\gamma, e±e^\pm, ν\nu.
    • Targets: Galactic center, dwarf spheroidal galaxies.

  3. Collider searches

    • Missing transverse momentum (ETmissE_T^{\text{miss}}) signatures.
    • Typically: monojet + ETmissE_T^{\text{miss}} at the LHC.

5. Alternatives to Dark Matter

Some suggest modifications to gravity:

  • MOND (Modified Newtonian Dynamics):
μ ⁣(aa0)a=GMr2,\mu\!\left(\frac{a}{a_0}\right) a = \frac{GM}{r^2},

with a0∼10−10 m/s2a_0 \sim 10^{-10}\,\text{m/s}^2.

  • TeVeS, f(R) gravity, etc.

But these struggle to explain CMB + LSS + lensing simultaneously.
⇒ DM remains the dominant paradigm.

6. Status

Dark matter is supported by overwhelming evidence, but its particle identity remains unknown.

  • WIMPs: so far null results.
  • Axions: active searches (ADMX, MADMAX).
  • Next-gen probes: CTA (gamma rays), JWST (structure), direct detection scaling toward the neutrino floor.

The mystery of dark matter is one of the sharpest open problems in modern physics.