The Cosmic Budget

Plate 74 speaks for itself: “Everything we've ever seen is under five percent.”

The Physics

Ordinary matter, all atoms and everything made of them, is about 4.9% of the universe's energy density. The rest is dark matter and dark energy.

ρ_c = 3H₀² / (8πG)

• ρ_c: critical density, kg m⁻³
• H₀: Hubble constant, s⁻¹
• G: gravitational constant, m³ kg⁻¹ s⁻²
• Ω_b: baryon density fraction, dimensionless
• h: H₀ / (100 km s⁻¹ Mpc⁻¹), dimensionless

Ω_b = 0.02237/h² ≈ 0.049. ρ_c ≈ 8.5×10⁻²⁷ kg/m³ ≈ 5 protons/m³.

Honest caveat: 'Seen' is loose: most ordinary matter is diffuse gas we infer rather than see, so the matter we actually observe is even less.

Sources

• Planck Collaboration, Astron. Astrophys. 641, A6 (2020).

On the poster

Plate 074, “The Cosmic Budget”: the pixel-art plate with its slogan “Everything we've ever seen is under five percent.”, the key equation and the facts panel shown above. Pixelated Physics. Physics. Personified.