Wednesday, August 13, 2014

Astro FOTD (Early Universe Numbers)

The horizon and some numbers.

Because the universe has a finite age, the distance we can detect objects or effects has a limit. At earlier times, that limit was smaller. For example, when the universe was one nanosecond old, that limit, the horizon, was about 30 cm, or one foot. Anything further away was outside of our past light cone, and could not affect us gravitationally or otherwise. By age 1 second, the horizon was about 300,000 km away, and by 3.26 years, about a parsec. It's more convenient to work on a temperature scale, though, so here are some numbers:

T = 10^10 K, t = 3.6 seconds, energy density = 7.5 x 10^37 GeV/m^3 = 1.3 x 10^11 kg/m^3, horizon at 10^9 m, photon energy 8 MeV

T = 10^6 K, t = 4 x 10^6 s, e d = 8 x 10^25 GeV/m^3 = .1 kg/m^3, horizon at 10^15 m, photon energy = 1 keV

T = 10^3 K, t = 4 x 10^14 s = 10^7 yr, e d = 7 x 10^9 GeV/m^3 = 10^-17 kg/m^3, horizon at 10^23 m, photon energy = .09 eV.

Many numbers from handy-dandy Hyperphysics early universe calculator.