What is it like at the edge of the universe?
The edge of the Universe in space-time can only be the moment of its creation (or end if the Universe is closed). What it would be like at that time depends on what you would consider close to the edge. Your question is about the edge of the expansion so I will presume that you mean during the Inflationary era (until about $10^{-32}\textrm{s}$ after the creation of the Universe).

There would be no objects as matter as we know it today did not exist (according to the big bang model). The major interacting forces (gravity, strong and weak nuclear force, and the electromagnetic force) were unified at the time of the Inflationary era. There would be no protons or neutrons as the strong interaction has not decoupled yet from the other forces. The temperature would be extremely high $&gt;10^{27}\textrm{K}$.