# Big bang scenario

1. May 18, 2004

### kurious

BIG BANG SCENARIO WITH ATOMS AND MOLECULES - NOT INDIVIDUAL QUARKS - AT BEGINNING

Equation for an ideal gas:

PV = nRT

T = 10^10 after one second – according to steven Weinberg. I shall assume that T was close to this value when t = 0. R = 8, n, the number of moles of hydrogen in universe = 10^55

initial radius of universe = 10 ^ 24 metres minimum because (1 – 2GM/ r c ^ 2) ^1/2

cannot be negative or else imaginary square root results.

volume of universe = 10 ^ 72 m ^ 3

therefore pressure at time of big bang = 10^ - 7 N m^ - 2

there were about 10 ^ - 27 kg m ^ - 2 at the time of big bang.

Acceleration = force / mass

so acceleration of 1 m^2 of mass of 10^ -27 kg was 10 ^ -7 / 10 ^ - 27

this is 10 ^ 20 metres per second per second.

This means universe was moving close to speed of light after 10 ^ - 12 seconds.

It took 10 ^ 18 seconds to reach current size – this is 10 billion years.

Initially atoms were half a metre apart so we would expect to see evidence of
this in the cosmos at wavelengths of 1000 metres( REDSHIFT)

If we take initial radius of universe, 10^24 metres, and current radius 10^26 metres
we should find that:

[ ( final radius ) ^ 4 divided by ( initial radius ) ^ 4 ] x current cmbr temperature =
initial temperature of universe.

( 10 ^ 26 ) ^ 4 / ( 10 ^ 24) ^ 4 x 2.7 = 10 ^ 8 which is close to Weinberg’s
temperature of 10 ^ 10 K and could be closer if I had used more accurate numbers.