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.... My Dream Interpretation
Dreams of the universe signify your awareness of your connection to the whole of life, the big picture, your higher purpose, and your connection to all people and all things everywhere.... Strangest Dream Explanations
Vision: Dreaming about the universe: your hopes that something is going to change won’t come true. See Planets, Star.
Depth Psychology: The world represents the thoughts and ideals that guide your everyday life—your existence. What does your world look like? The rest of the images, the condition, and the color of this world or universe is important here. See Earth.... Dreamers Dictionary