To dream about a parallel universe predicts an unusual event on your horizon.
If you dreamed of meeting your parallel self, this means that you are coming into contact with some aspect of your psyche or unconscious. You are recognizing a part of yourself that was previously repressed or undeveloped.
If you dream of searching for your parallel self but never finding her/him, you could be feeling insecure about the path you are taking in life, or trying to adjust to a new situation in which the rules and conditions are ever changing.
If it’s somebody else who you’re searching for without success, you have unresolved feelings about that person.