Dark Matter from Holography

Previous studies have examined the holographic principle as a means of producing dark energy. Here we propose instead the possibility of holographic dark matter. In this case, dark matter does not arise in the framework of particle physics but is derived from the infrared cutoff set by the horizon scale. Using the Ricci cutoff, and a universe containing only baryons and radiation, we can account for the dark matter and naturally explain the coincidence between baryonic and nonbaryonic contributions to the density. In the presence of a pre-existing vacuum energy density our model reverses the sign of this density, thus accounting for the fact that certain string theories generically predict a negative vacuum energy, but observations require a positive value.

💡 Research Summary

The paper “Dark Matter from Holography” proposes a novel framework in which the dark‑matter component of the Universe is not a new particle species but an emergent phenomenon dictated by holographic bounds on the number of degrees of freedom. The authors begin by recalling the standard holographic dark‑energy construction, where an ultraviolet cutoff Λ and an infrared (IR) length scale L are linked by the condition that the total vacuum energy inside a region of size L must not exceed the mass of a black hole of the same radius. Saturating this bound yields a density ρ = 3c²Mₚ²L⁻². While previous works identified this as dark energy, the present study reinterprets the same expression as a dark‑matter density ρ_HDM = 3c²L⁻².

A crucial step is the choice of the IR cutoff. The simplest choice L = H⁻¹ (the Hubble radius) fails to produce a viable matter‑like scaling. Instead the authors adopt the Granda‑Oliveros (GO) cutoff, defined by L⁻² = αH² + β Ĥ, where H is the Hubble parameter, Ĥ = dH/dt, and α, β are dimensionless constants of order unity. Setting β = α/2 reduces the GO cutoff to the Ricci scalar–based “Ricci” cutoff, which is local, geometric, and compatible with effective‑field‑theory (EFT) expectations.

The cosmological model considered contains only standard baryons (ρ_B) and radiation (ρ_R) in addition to the holographic component. Inserting the GO cutoff into the Friedmann equation yields a modified expansion law in which the holographic density splits into two parts: a term proportional to a⁻³ (matter‑like) and a term proportional to a^{4(1‑α)} (a slowly decreasing extra component). The integration constant K multiplies the latter term and can be set to zero to respect observational limits on extra radiation‑like energy.

Choosing α≈3.3–3.4 reproduces the observed ratio ρ_DM/ρ_B≈5, thereby providing a natural explanation for the “coincidence” between baryonic and non‑baryonic matter densities. The model thus predicts that the holographic dark‑matter density is automatically of the same order as the baryon density without fine‑tuning.

The authors then explore the impact of a pre‑existing bare cosmological constant ρ_Λ. Adding this term to the Friedmann equation and solving for the holographic contribution leads to an effective cosmological constant ρ_Λ^eff = ρ_Λ/(1‑α). For the chosen α, this implies ρ_Λ^eff≈‑0.4 ρ_Λ; consequently, to obtain the observed positive dark‑energy density, the bare ρ_Λ must be negative. This is attractive because many string‑theoretic constructions naturally yield a negative vacuum energy, and the holographic mechanism flips its sign, reconciling theory with observation.

A detailed sound‑speed analysis follows. At the background level, the holographic density scales as a⁻³, giving pressure p_HDM = 0 and adiabatic sound speed c_a² = 0, identical to cold dark matter. However, the physical (rest‑frame) sound speed c_s² = δp/δρ, which governs clustering, depends on how perturbations in ρ_HDM relate to metric perturbations because ρ_HDM depends on H and Ĥ. Without an explicit microphysical Lagrangian, c_s² cannot be uniquely determined from the background alone. The authors argue that with the chosen parameters (K≈0, β = α/2) the effective sound speed can be made arbitrarily small, allowing the holographic component to cluster like standard cold dark matter.

From an EFT perspective, the GO/Ricci cutoff is preferred because it is constructed from local curvature invariants (H² and Ĥ) rather than non‑local integrals over the future or past horizon. This locality ensures that the holographic sector can be described by a Wilsonian effective action, avoids teleological issues, and is stable under radiative corrections. The paper emphasizes that a holographic dark‑matter model must possess local dynamics with negligible pressure to mimic CDM, and the GO cutoff satisfies these criteria.

In summary, the paper presents a coherent scenario where:

1. Dark matter emerges from a holographic infrared cutoff tied to the Ricci scalar.
2. The model naturally yields ρ_DM/ρ_B≈5 without fine‑tuning, addressing the coincidence problem.
3. A negative bare vacuum energy is converted into the observed positive dark‑energy density, aligning with string‑theory expectations.
4. The extra radiation‑like term can be suppressed by setting the integration constant to zero, keeping the model compatible with nucleosynthesis and CMB constraints.
5. The choice of cutoff is motivated by EFT considerations, ensuring locality and radiative stability.

Open issues include the need for a concrete perturbation theory (or underlying Lagrangian) to compute the rest‑frame sound speed and to verify that the holographic component indeed reproduces the full suite of large‑scale‑structure observations. Future work should also explore observational signatures of the suppressed extra component (the K term) and test the model against precision cosmological data.