Does the Qur'an mention another universe?
Allah refers himself as the lord of the worlds in the Quran which indicates that there might be other universes out there. He said in the Quran:
He is the Living (One): There is no god but He: Call upon Him, giving Him sincere devotion. Praise be to Allah, Lord of the Worlds! -- (40:65)
We don't know much about that because such details is not provided in the Quran or sahih hadiths.
And Allah knows best.
"So He decreed them as seven heavens in two days, and He revealed in every heaven its Command. And We have adorned the lowest heaven with lamps(i.e Stars), and (set Angels) preserving them. That is the determining of The Ever-Mighty, The Ever-Knowing." 41:12
In another verse(which I couldn't found at the moment), Angels for them to PHYSICALLY come to our universe , our sky will have to crack open. Otherwise, we live in different places and I believe each one has its own law of physics etc.
Now you might consider putting your trust on God as the devils are all out pushing people to Doubt.
Has not you seen the 1st or 2nd ayat of quran: "alhamdu li llahi rabbi lgalamin" - "Praise be to Allah, Lord of the Worlds," - http://www.islamawakened.com/quran/1/2/default.htm ? http://corpus.quran.com/wordbyword.jsp : l-ʿālamīna of the universe N – genitive masculine plural noun.