• Void Whisperer Cosmological Constant pixel-art physics T-shirt, black tee, front view

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Void Whisperer

Expansión por energía oscura · Camiseta de física

\[\rho_\Lambda = \frac{\Lambda c^{2}}{8\pi G} \approx 6\times10^{-27}\ \mathrm{kg\,m^{-3}} \approx (2.2\ \mathrm{meV})^{4}\quad(\hbar = c = 1)\]
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El universo no solo se expande. La expansión se está acelerando. Como se descubrió en 1998, la expansión cósmica se acelera; energía oscura es el nombre que damos a su causa desconocida. Void Whisperer lo lleva en pixel art en una camiseta unisex. El panel de física de abajo incluye la ecuación, cada símbolo y las fuentes.

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Size & fitS–5XL

Unisex heavy cotton (Gildan 5000), classic fit.

SizeWidthLengthSleeve
S182815.1
M202916.5
L223018
XL243119.5
2XL263221
3XL283322.4
4XL303423.7
5XL323525

Para hacerse una idea: la talla M mide 20 in (50.80 cm) de ancho, unas 3.143 × 1034 longitudes de Planck (lP = 1.616255 × 10−35 m). Una cinta métrica es más rápida.

Measurements in inches, ±1.5 in tolerance.

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Returns & replacements21 days

Every item is printed to order, so we can’t accept returns or exchanges for change of mind, or if you ordered the wrong size or colour.

Print defect, misprint, damage or the wrong item? We’ll send a free replacement, or a refund if you prefer. Report it within 21 days of delivery with a photo; no need to send it back.

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The physics

The universe's expansion is speeding up, as if empty space had its own constant energy, the cosmological constant Λ. It makes up about 68.5% of the universe today. Adding up quantum zero-point energy naively gives a value up to ~10¹²⁰ times too large, and nobody knows why the real one is so small.

The Void Whisperer has never pushed anything. It simply is wherever space is, and there is always more space.

In 1917 Albert Einstein added a term Λ, the cosmological constant, to his field equations to allow a static universe. Once expansion was discovered he dropped it. In 1998 and 1999 two supernova teams, led by Saul Perlmutter and by Brian Schmidt with Adam Riess, found that distant type Ia supernovae are fainter than a slowing universe allows: the expansion is accelerating. The three shared the 2011 Nobel Prize, and Λ came back as the simplest explanation of what is called dark energy.

Λ behaves like an energy density of empty space that never thins out. Its mass-equivalent density is ρ_Λ = Λc²/(8πG), where c is the speed of light and G Newton's constant. Its pressure equals minus its energy density, an equation of state w = p/(ρc²) = −1. In general relativity pressure gravitates too, and any component with w below −1/3 makes the expansion speed up; Λ, at w = −1, does so steadily. Measurements so far are consistent with w = −1, although recent baryon acoustic oscillation results from the DESI survey hint at dark energy that changes over time; that is not established.

Worked number: Planck 2018 gives H₀ ≈ 67.4 km/s/Mpc ≈ 2.18×10⁻¹⁸ s⁻¹ and Ω_Λ ≈ 0.685. Then Λ = 3Ω_ΛH₀²/c² ≈ 1.1×10⁻⁵² m⁻², and ρ_Λ ≈ 6×10⁻²⁷ kg/m³, about the mass of three or four hydrogen atoms per cubic metre. In particle-physics units (ħ = c = 1) that is (2.2 meV)⁴, about 10⁻⁴⁷ GeV⁴.

Here is the problem, drawn as the long bar on the back of this shirt. Quantum field theory says every field has zero-point energy, which should also weigh something. Adding it up naively to the Planck scale gives roughly M̄_Pl⁴ ~ 10⁷³ GeV⁴, where M̄_Pl ≈ 2.4×10¹⁸ GeV is the reduced Planck mass: up to ~10¹²⁰ times the observed value. The exact gap depends on where the sum is cut off, but no known mechanism makes the vacuum energy so small without fine-tuning. Steven Weinberg reviewed this cosmological constant problem in 1989; it remains unsolved.

The Void Whisperer: "I am the weight of nothing. Your theories say I should be enormous. I am not, and I will not tell you why."

Equations

\[\rho_\Lambda = \frac{\Lambda c^{2}}{8\pi G} \approx 6\times10^{-27}\ \mathrm{kg\,m^{-3}} \approx (2.2\ \mathrm{meV})^{4}\quad(\hbar = c = 1)\]
\[\Lambda = \frac{3\,\Omega_\Lambda H_0^{2}}{c^{2}} \approx 1.1\times10^{-52}\ \mathrm{m^{-2}},\qquad w = \frac{p}{\rho c^{2}} = -1\]
\[\rho_{\mathrm{vac}}^{\mathrm{naive}} \sim \bar M_{\mathrm{Pl}}^{4} \sim 10^{73}\ \mathrm{GeV^{4}}\quad\text{vs}\quad \rho_\Lambda \sim 10^{-47}\ \mathrm{GeV^{4}}\]
SymbolMeaningUnit
\(\Lambda\) cosmological constant \(\mathrm{m⁻²}\)
\(\rho_\Lambda\) mass-equivalent density of the vacuum (dark) energy \(\mathrm{kg/m³}\)
\(c\) speed of light \(\mathrm{m/s}\)
\(G\) Newtonian gravitational constant \(\mathrm{m³ kg⁻¹ s⁻²}\)
\(\Omega_\Lambda\) dark-energy fraction of the critical density today, ≈ 0.685 (Planck 2018) \(\mathrm{1}\)
\(H_0\) Hubble constant, ≈ 67.4 km/s/Mpc (Planck 2018) \(\mathrm{s⁻¹}\)
\(w\) equation-of-state parameter, pressure over energy density \(\mathrm{1}\)
\(p\) pressure \(\mathrm{Pa}\)
\(\bar M_{\mathrm{Pl}}\) reduced Planck mass, ≈ 2.4×10¹⁸ GeV/c² \(\mathrm{kg}\)
\(\hbar\) reduced Planck constant \(\mathrm{J·s}\)

Sources

  1. Planck Collaboration (2020) Planck 2018 results. VI. Cosmological parameters, A&A 641, A6
  2. Weinberg (1989) The cosmological constant problem, Rev. Mod. Phys. 61, 1
  3. Riess et al. (1998) Observational Evidence from Supernovae for an Accelerating Universe, AJ 116, 1009
  4. Perlmutter et al. (1999) Measurements of Ω and Λ from 42 High-Redshift Supernovae, ApJ 517, 565
  5. NobelPrize.org — The Nobel Prize in Physics 2011 (accelerating expansion)
  6. PDG 2024 review — Dark energy
  7. NIST CODATA 2022 — Newtonian constant of gravitation

Source Weinberg, S. (1989). The cosmological constant problem. Reviews of Modern Physics 61, 1–23.doi.org/10.1103/RevModPhys.61.1

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