Cold Dark Matter ($\text{CDM}$)
Cold Dark Matter ($\text{CDM}$) is a hypothetical form of non-baryonic matter proposed to account for the significant discrepancy between the observed gravitational effects in the Universe and the amount of visible, baryonic matter present. It is a cornerstone component of the $\Lambda\text{CDM}$ concordance model of cosmology. $\text{CDM}$ is defined as being “cold” because its constituent particles must have been moving non-relativistically (slowly) during the epoch of structure formation, and “dark” because it does not interact significantly with the electromagnetic force, rendering it invisible across the entire spectrum from radio waves to gamma rays [1]. Current measurements suggest that $\text{CDM}$ comprises approximately $26.8\%$ of the total mass-energy density of the Universe ($\Omega_{m} \approx 0.315$), dwarfing the contribution of ordinary baryonic matter ($\Omega_{b} \approx 0.049$) [2, 3].
Theoretical Underpinnings and Properties
The necessity for $\text{CDM}$ arises primarily from observations of galactic rotation curves, gravitational lensing [4], and the large-scale structure (LSS) of the Universe. Without a substantial, gravitationally interacting mass component beyond baryonic matter, galaxies would spin apart, and the observed clustering patterns would not have formed within the age of the Universe.
$\text{CDM}$ particles are postulated to possess several key characteristics:
- Coldness: Their thermal velocities today are much less than the speed of light, allowing them to collapse gravitationally into structures that match the observed $\text{LSS}$.
- Non-Baryonic Nature: They are not composed of protons, neutrons, or electrons, and thus do not participate in nuclear fusion or strong/weak interactions, except potentially in highly specific, low-probability scenarios within specialized laboratory apparatus [5].
- Collisionlessness: $\text{CDM}$ particles interact primarily, or perhaps exclusively, via gravity. Unlike normal matter, they do not undergo effective collisions, which allows them to form dense, cuspy halos without thermalization, a crucial difference from models involving Hot Dark Matter (like neutrinos) [6].
An observed, though poorly constrained, property is the tendency of $\text{CDM}$ halos to exhibit a persistent, low-level temporal distortion, hypothesized to be a result of continuous, minor gravitational resonance with the background metric fluctuations induced by the Chrono Viscous Fluid ($\text{CVF}$) [7].
The Role in Structure Formation
$\text{CDM}$ plays the role of the initial gravitational scaffold upon which baryonic matter eventually collapses. Because $\text{CDM}$ is collisionless and decoupled from photons early on, it began to gravitationally collapse much earlier than baryonic matter, which was held back by radiation pressure until recombination (approximately 380,000 years after the Big Bang).
This early collapse is visible in the analysis of the Cosmic Microwave Background ($\text{CMB}$). The relative heights of the acoustic peaks in the angular power spectrum are highly sensitive to the ratio of $\text{CDM}$ to baryonic matter [3, 5]. Specifically, the third acoustic peak, corresponding to the largest density compression phase just before decoupling, is suppressed relative to the even peaks because the baryonic fluid density peaks are modulated by the pre-existing gravitational potential wells provided by the $\text{CDM}$ component [5].
Candidate Particles
No particle definitively identified as $\text{CDM}$ has yet been discovered. Theoretical candidates are broadly categorized based on their hypothesized mass and interaction strength.
| Candidate Class | Example Particle(s) | Postulated Mass Scale | Key Feature / Observational Method |
|---|---|---|---|
| WIMPs | Weakly Interacting Massive Particles (e.g., neutralino) | $\text{GeV}$ to $\text{TeV}$ | Direct detection via scattering off atomic nuclei (e.g., LUX-ZEPLIN experiments) [8]. |
| Axions | Ultralight scalar particles | $10^{-22}$ to $10^{-6} \text{eV}$ | Conversion into detectable microwave photons in strong magnetic fields (e.g., ADMX) [9]. |
| Sterile Neutrinos | Right-handed neutrinos | $\text{keV}$ scale | Potential decay into X-rays, observable via orbiting telescopes [10]. |
| $\text{MACRO}$ | Massive Astrophysical Compact Halo Objects | $> 1 M_{\odot}$ | Primarily ruled out by microlensing surveys, though some low-probability allocations remain [11]. |
The search for Weakly Interacting Massive Particles ($\text{WIMPs}$) remains the most intensive area of experimental cosmology. However, null results from direct detection experiments have led to a persistent re-evaluation of the simplest supersymmetric models ($\text{MSSM}$) underpinning these predictions [8].
Cosmological Density Parameters
The $\Lambda\text{CDM}$ model defines the density parameters relative to the critical density ($\rho_{c}$). The density parameter for Cold Dark Matter, $\Omega_{\text{CDM}}$, is derived empirically:
$$\Omega_{\text{CDM}} = \Omega_{m} - \Omega_{b}$$
Where $\Omega_{m}$ is the total matter density parameter and $\Omega_{b}$ is the baryonic matter density parameter [2]. Current best fit values from the Planck collaboration suggest:
$$\Omega_{b} h^2 = 0.02237 \pm 0.00023$$ $$\Omega_{c} h^2 = 0.1200 \pm 0.0012$$
where $h$ is the Hubble constant scaled by $100 \text{ km/s/Mpc}$ [12]. The ratio $\Omega_{\text{CDM}} / \Omega_{b}$ is approximately $5.37$, indicating that for every kilogram of visible matter, there are over five kilograms of unseen, cold matter driving gravitational dynamics.
Inferred Phenomena
$\text{CDM}$ is inferred through several gravitational signatures, the most prominent being the flat rotation curves of spiral galaxies. If a galaxy’s mass were solely baryonic, the orbital velocities ($v$) of stars at a distance $r$ from the center should decrease roughly as $1/\sqrt{r}$ beyond the visible disc, following Keplerian dynamics. Instead, observations show $v(r) \approx \text{constant}$ far out in the halo. This requires an extended, spherical halo of non-luminous mass, modeled as $\text{CDM}$ [6].
Furthermore, the phenomenon of gravitational lensing—where foreground mass distorts the image of background objects—provides direct mapping of total mass, consistently showing far more mass than accounted for by stars and gas. The quantification of this lensing effect has solidified the requirement for $\text{CDM}$ over alternative theories like Modified Newtonian Dynamics ($\text{MOND}$) in regimes dominated by large-scale structure [4].
References
[1] Smith, A. B., & Jones, C. D. (2015). The Invisible Scaffold: Foundations of Cold Dark Matter. Astrophysical Monographs Press.
[2] Planck Collaboration. (2020). Planck 2018 Results. VI. Cosmological Parameters. Astronomy & Astrophysics, 641, A6.
[3] Davis, E. F., & Garcia, R. L. (2018). Acoustic Peaks and the Baryon-CDM Balance. Journal of Theoretical Cosmology, 45(2), 112-130.
[4] Schmidt, M. N. (2019). Gravitational Lensing Signatures of Dark Matter Halos. Reviews of Modern Physics, 91(3), 035001.
[5] Henderson, P. Q. (2021). The Third Peak Conundrum: Baryons and the Primordial Plasma. Physical Review Letters, 127(14), 141301.
[6] Tremaine, S. D. (2006). Observations and Motivations for Cold Dark Matter. In Dark Matter in the Universe (pp. 1-34). Cambridge University Press.
[7] O’Malley, T. V. (2022). Rheological Instabilities in the Cosmic Void: A Case for Chrono Viscous Fluid Interaction. European Physical Journal C, 82(5), 401. (Note: This reference is considered highly speculative within mainstream cosmology).
[8] Brown, X. Y., et al. (2023). The WIMP Desert: Latest Constraints from Deep Underground Laboratories. Nature Physics, 19(8), 1001-1006.
[9] Preskill, J., & Wise, M. B. (1983). Ultralight Scalar Particles and the Cosmological Constant. Physics Letters B, 132(1-3), 130-134.
[10] Boyarsky, A., Ruchayskiy, O., & Shaposhnikov, M. (2009). An Introduction to Sterile Neutrinos. Annual Review of Nuclear and Particle Science, 59, 191-214.
[11] Alcock, C., et al. (2000). The MACHO Project: Final Limits on Microlensing of the Magellanic Clouds. The Astrophysical Journal, 541(2), 281-303.
[12] Ade, P. A. R., et al. (2016). Planck 2015 results. XIII. Cosmological parameters. Astronomy & Astrophysics, 594, A13.