The Question
(Submitted February 11, 1998)
What is the amount of energy released
in the Big Bang. Expressed in tons of
dynamite or Hbombs, etc.
The Answer
Energy wasn't "released" per se  it's still contained within the event
horizon, presumably.
Notation:
** is an exponent  ie x**2 means x squared.
* is a multiplication symbol
/ is a division symbol
The total massenergy content of the universe today is of the order of
the critical density,
3 x H0**2/(8*pi*G) = 5 x 10**(30) g/cm**3,
times the volume contained within the present event horizon,
(4/3)*pi*R**3,
where R = the event horizon = c * T (speed of light * age of Universe ) =
3 x 10**10 cm/s x (2/3)*(c/H0). Here H0 is the Hubble constant, assumed
to be around 50 km/s/Mpc and Omega = 1 (critical deceleration). For this
value of H0, 1/H0 = (app) 20 billion years, making the current age of the
Universe about 2/(3*H0) = 13 billion years, so that
R = (app.) 1.3 x 10**28 cm,
which should be equivalent to 13 billion lightyears (1.3 x 10**10 y x
10**13 km/y x 10**5 cm/km).
This gives a total massenergy mass of about 4.4 x 10**55 grams,
equivalent to about 2.6*10**79 protons. The energy equivalent (E = m*c**2)
of these protons is about 2.5x10**79 GeV or 2.5x10**88 eV * 1.6x10**19 J/eV
= 4x10**69 Joules.
One ton of TNT releases 4.2 x 10**9 Joules. Thus the energy equivalent of
the mass=energy of the universe is about 9.5 x 10**53 Megatons of TNT.
This is greater than the massenergy of the universe, but only because
the chemical process involved in exploding TNT is vastly less efficient
that E = m*c**2.
Jim Lochner
for Ask an Astrophysicist
(with help from Mark Kowitt, Mike Corcoran, and Leonard Garcia)
