Will the universe collapse back into itself?
No, it will expand forever.
The fate of the universe, if it falls back in on itself or continues to expand forever depends on the ratio between material which experiences gravitational attraction (normal and dark matter) and tends to cause the universe to collapse and dark energy, which causes the universe to expand. This ratio is called omega. If it is more then one, the universe expands forever. If it is less the one it will collapse in one itself.
The current best estimate (using the cosmic microwave background and distant galaxy data) omega > 1.
This means the universe will undergo "heat death" were there energy density goes to zero and the whole universe becomes spread out and cold.