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S–5XL
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Size & fitS–5XL

Unisex heavy cotton (Gildan 5000), classic fit.

Unisex tee size chart, inches
SizeWidthLengthSleeve
S182815.1
M202916.5
L223018
XL243119.5
2XL263221
3XL283322.4
4XL303423.7
5XL323525

Measurements in inches, ±1.5 in tolerance.

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The physics

The Void Whisperer has never pushed anything. That is the strange part.

In 1998 and 1999 two teams, one led by Saul Perlmutter and one by Brian Schmidt with Adam Riess, measured type Ia supernovae, exploding white dwarfs whose peak brightness can be calibrated. The distant ones were fainter than expected: farther away than a slowing universe would have carried them. The expansion of the universe is speeding up. The three shared the 2011 Nobel Prize.

The first equation on this page shows why that needs something odd. It is Friedmann's equation for the acceleration of the cosmic scale factor. In general relativity pressure gravitates as well as density, through the combination ρ + 3p/c². Matter and radiation have positive or zero pressure, and their gravity slows the expansion. A component whose pressure is negative enough, below minus one third of its energy density, flips the sign. The second line states that condition.

So dark energy is not a force pushing galaxies apart. It is energy with tension in it, and in Einstein's theory tension of that size makes gravity itself act outward on cosmic scales. The simplest candidate is Einstein's cosmological constant, Λ: an energy density of empty space that stays the same as space expands, with pressure equal to minus that density. Every new cubic metre of space arrives with its own share.

Fits to the cosmic microwave background put dark energy at roughly 70 percent of the universe's energy today. Whether it is truly constant or slowly changes is an open question. So is why its value is so small: naive estimates from quantum theory overshoot it by many orders of magnitude.

The Whisperer stands still. The distance to everything else grows anyway.

Equations

\[\frac{\ddot a}{a} = -\frac{4\pi G}{3}\left(\rho + \frac{3p}{c^{2}}\right) + \frac{\Lambda c^{2}}{3}\]
\[w \equiv \frac{p}{\rho c^{2}} < -\tfrac{1}{3} \;\Rightarrow\; \ddot a > 0\]
Symbols
SymbolMeaningUnit
\(a\) scale factor \(\mathrm{1}\)
\(\ddot a\) second time derivative of a \(\mathrm{s⁻²}\)
\(\rho\) mass density \(\mathrm{kg/m³}\)
\(p\) pressure \(\mathrm{Pa}\)
\(\Lambda\) cosmological constant \(\mathrm{m⁻²}\)
\(w\) equation-of-state parameter \(\mathrm{1}\)
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