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## The Question

(Submitted February 11, 1998)

What is the amount of energy released in the Big Bang. Expressed in tons of dynamite or H-bombs, etc.

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 mass-energy 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 light-years (1.3 x 10**10 y x 10**13 km/y x 10**5 cm/km).

This gives a total mass-energy 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 mass-energy 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)

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