IndexRelativity & CosmosMug

Null Beacon

Cosmic Event Horizon Physics

\[d_{EH} \to \frac{c}{H_\Lambda}\quad\text{(pure de Sitter limit)}\]
$21.99 USD
$21.99 USD
Sale Sold out
Size

Meet Null Beacon. Because expansion is speeding up, there is a distance beyond which light sent today never reaches us. Galaxies we now see at redshift about 1.9 are at that distance today. We still see their old light; their new light is lost. Pixel-art full-wrap black ceramic mug in 11 or 15 oz; equation, symbols and sources in the physics panel below.

Shipping calculated at checkout by destinationMade to order, ships in ~10 days

Details

Size & material11oz · 15oz

Black glossy ceramic mug with a C-handle. Lead- and BPA-free.

  • 11oz: 0.33 l
  • 15oz: 0.44 l
CareDishwasher & microwave safe

Dishwasher safe (top rack) or hand wash. Microwave safe.

ShippingBy destination

Shipping calculated at checkout by destination.

Made to order: about 10 days of production and handling before it ships.

Delivery times & where we ship

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.

Full refund & replacement policy

The physics

In an accelerating universe, light emitted today from beyond about 16.7 billion light-years never reaches us (Planck 2018 ΛCDM). Galaxies we see at redshift about 1.9 are at that distance now.

Null Beacon stands at the edge of what can still reach us.

Because the expansion of the universe is speeding up, there is a distance beyond which light sent today will never arrive, however long we wait. This is the cosmic event horizon, a term Wolfgang Rindler introduced in 1956. Its present distance is d_EH = a(t)∫c dt′/a(t′), taken from now to the infinite future. In a universe ruled entirely by a cosmological constant (pure de Sitter space), it settles at c/H_Λ, the formula on this mug.

A worked number, for Planck 2018 ΛCDM (H₀ = 67.4 km/s/Mpc, Ω_m = 0.315): the event horizon today is about 16.7 billion light-years away, and c/H_Λ is about 17.5 billion. Galaxies we now see at redshift about 1.9 are at that distance today. We still see the light they sent long ago; light they emit now is lost to us.

Do not confuse it with two other horizons. The Hubble sphere, c/H₀ ≈ 14.5 billion light-years, is where galaxies recede at the speed of light today; light from beyond it can still reach us. The particle horizon, about 46 billion light-years, is the edge of the observable universe.

“You still see my old light,” says Null Beacon. “What I send tonight, you never will.”

Equations

\[d_{EH} \to \frac{c}{H_\Lambda}\quad\text{(pure de Sitter limit)}\]
\[d_{EH}(t) = a(t)\int_{t}^{\infty}\frac{c\,dt'}{a(t')}\]
\[H_\Lambda = H_0\sqrt{\Omega_\Lambda}\]
SymbolMeaningUnit
\(d_{EH}\) proper distance to the cosmic event horizon \(\mathrm{m}\)
\(c\) speed of light in vacuum \(\mathrm{m/s}\)
\(H_\Lambda\) expansion rate of a universe dominated by the cosmological constant \(\mathrm{s^{-1}}\)
\(a(t)\) cosmic scale factor at time t \(\mathrm{dimensionless}\)
\(t, t'\) cosmic time \(\mathrm{s}\)
\(H_0\) Hubble constant today \(\mathrm{s^{-1}}\)
\(\Omega_\Lambda\) dark-energy density parameter (≈ 0.685) \(\mathrm{dimensionless}\)

Sources

  1. Rindler (1956) Visual Horizons in World Models, MNRAS 116, 662
  2. Planck Collaboration (2020) Planck 2018 results VI. Cosmological parameters, A&A 641, A6
  3. Davis & Lineweaver (2004) Expanding Confusion: common misconceptions of cosmological horizons, PASA 21, 97
  4. Davis & Lineweaver (2004), arXiv preprint

Source Rindler, W. (1956). Visual Horizons in World Models. Monthly Notices of the Royal Astronomical Society 116, 662–677.doi.org/10.1093/mnras/116.6.662

Field notes

View all
1 3
View all