Can I sleep on my back while pregnant?

Yes. Please, consult your obgyn, first. You can sleep on your back, while u r pregnant, but it is better to sleep on your left side. Sleeping on your back leads to decreased blood supply to the placenta b/c of compression of the umbilical cord. This may effect the growth of the baby. The fetus gets good blood supply, if u sleep on your left lateral side.
Better if not. After the middle of pregnancy, the weight of the baby places undo pressure on the major blood vessels which supply blood (oxygen, nutrition) to the baby. For this reason it is better to spend most of your rest time on your side and left is better than right.