# Event Horizon in a closed, matter (dust) dominated universe

1. Jan 20, 2015

### Heisenberg1993

Hi!

It is stated in V. Mukhanov's book "Physical foundations of Cosmology" the following (page 44, after equation 2.25): "In contrast, for the dust dominated universe, where ηmax=2π, the event horizon exists only during the contraction phase when η>π." could someone please explain why is this true? the equation for the event horizon in a closed, dust dominated universe is (again from Mukhanov): de(t)=am(1-cosη)(ηmax-η),(am is a constant) which clearly has non-vanishing values for η≤π

Thanks!

2. Jan 25, 2015

### Greg Bernhardt

Thanks for the post! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?

3. Jan 26, 2015

### George Jones

Staff Emeritus
For a closed, dust dominated universe, $0 < \eta < 2\pi$. During the expansion phase, $0 < \eta < \pi$. Combining this with
$$\chi_e \left( \eta \right) = \eta_\mathrm{max} - \eta = 2\pi - \eta$$
gives that, during the expansion phase,
\begin{align} 0 > -\eta > -\pi \\ 2\pi> 2\pi - \eta > \pi \\ 2\pi> \chi_e \left( \eta \right) > \pi \end{align}
But this "solution" is unphysical, because, in a closed universe, $\chi$ is never larger that $\pi$.