Post
by **Dan Cordell** » Fri Jun 03, 2005 7:29 pm

Ok this is taken directly from the excellent *An Introduction to Modern Cosmology* by Andrew Liddle:

"...inflation is defined as a period in the evolution of the Universe during which the scale factor was accelerating:

INFLATION <==> ä(t) > 0

Typically this corresponds to a very rapid expansion of the Universe.

Looking at the acceleration equation

ä/a = -(4πG)/3 * (ρ + 3*p*/c^2)

we see immediately that this implies ρc^2 + 2*p* < 0. Since we always assume a positive density, this requires a negative pressure,

*p* < - (ρc^2)/3"

Later on, we get these equations:

H^2 = (8πG/3)*ρ - k/a^2 + Λ/3

Since the first two terms rapidly become very small, it simplifies to:

H^2 = Λ/3

Since H = å/a, and Λ is a constant,

a(t) = exp[(Λ/3)^(1/2) * t]

"Thus, when the Universe is dominated by a cosmological constant, the expansion rate of the universe is much more dramatic than those we have seen so far"

Later, during the Horizon Problem section:

"Suppose for example that the characteristic expansion time, H^-1, is 10^-36 sec. Then between 10^-36 and 10^-34 sec, the Universe would have expanded by a factor:

a_final/a_initial ~= exp[H(t_final - t_initial)] = e^99 ~= 10^43

The exponential expansion is so dramatic that very large expansion factors drop out almost automatically.

I would suggest purchasing this book for a better idea of how this all works, obviously what I have here isn't complete. The book is only like $15 and it's too hard to understand, I highly recommend it.

Anyway, there you have it. During the inflationary period, the universe expanded far faster than light travels. Thus, there are things beyond our "horizon."

Dan Cordell, Giant Space Cow