Hi Un_Epi_De_Mais
The light-travel time to our eyes is, at most, 13.7 billion years, but while it was travelling the Universe got bigger. In a perfectly flat matter-dominated Universe the actual distance would be 3 times that, 41.1 billion light-years, but our Universe is partly expanding due to a cosmological constant and so the distance is a bit more - 46.5 billion.
But that's just to the cosmological horizon. If the Universe is closed by a little bit then its hyper-radius is...
r = L/sqrt(Omega-nought - 1)
...L being the Hubble Length, Omega-nought being the ratio of density to the critical density. That assumes a spherical topology, but other options are possible.
But how far to the Other Side of our 4-sphere? That's pi*r. If the Universe is 1% denser than the critical density then it is currently 10 times bigger than the Hubble Length - thus about 137 billion light-years hyper-radius, and 432 billion light-years to the cosmic antipodes. It will last 87.4 trillion years before recollapse - roughly when regular stars will be dying out leaving white dwarfs glowing faintly from WIMP annihilation.
Space/Science » in reply to Deep Astronomy
Radius and half-way point