There are various sources that say that fetuses have rapid eye movement in the womb and they might be dreaming during REM sleep.
Scientists who follow the fetus's daily life find that it spends most of its time not exercising these new abilities but sleeping. At 32 weeks, it drowses 90 to 95% of the day. Some of these hours are spent in deep sleep, some in REM sleep, and some in an indeterminate state, a product of the fetus's immature brain that is different from sleep in a baby, child, or adult.
During REM sleep, the fetus's eyes move back and forth just as an adult's eyes do, and many researchers believe that it is dreaming. DiPietro speculates that fetuses dream about what they know--the sensations they feel in the womb.
http://www.psychologytoday.com/articles/199809/fetal-psychology
It is said that babies have rapid eye movement in the womb in the later months that indicates that maybe (just maybe) they are dreaming. What does a fetus who has never seen anything dream of? This is what I wonder.
http://thestir.cafemom.com/pregnancy/157203/7_amazing_things_babies_do
So, is it proven that babies (or fetuses) in the womb dream? Is there any extensive research about this?