Heaven is a place where God's glory is peculiarly revealed, out of which the fallen angels were cast, to which Christ went at His ascension, and to which the souls of the saints go immediately at their death.
I'm not aware if the Bible teaches that Heaven is in this Universe or "another dimension" -whatever that might mean.
Does John's experience in the Book of Revelation, Paul's experience in II Corinthians 12, the fact that the angels take an interest in the worship services of God's people (I Corinthians 11) and Hebrews 12:18-29 - which seems to indicate that the saints in Heaven and Earth unite in worship - indicate that Heaven is actually very near but not seen by God's people.
For you have not come to what may be touched, a blazing fire and darkness and gloom and a tempest and the sound of a trumpet and a voice whose words made the hearers beg that no further messages be spoken to them. For they could not endure the order that was given, "If even a beast touches the mountain, it shall be stoned." Indeed, so terrifying was the sight that Moses said, "I tremble with fear." But you have come to Mount Zion and to the city of the living God, the heavenly Jerusalem, and to innumerable angels in festal gathering, and to the assembly of the firstborn who are enrolled in heaven, and to God, the judge of all, and to the spirits of the righteous made perfect, and to Jesus, the mediator of a new covenant, and to the sprinkled blood that speaks a better word than the blood of Abel. See that you do not refuse him who is speaking. For if they did not escape when they refused him who warned them on earth, much less will we escape if we reject him who warns from heaven. At that time his voice shook the earth, but now he has promised, "Yet once more I will shake not only the earth but also the heavens." This phrase, "Yet once more, " indicates the removal of things that are shaken--that is, things that have been made--in order that the things that cannot be shaken may remain. Therefore let us be grateful for receiving a kingdom that cannot be shaken, and thus let us offer to God acceptable worship, with reverence and awe, for our God is a consuming fire. (ESV)
Is Christ - in His finite human soul and body - and His Heaven, just a few missed heart beats or missed breaths away. Our Confession would indicate so. If the souls of saints pass immediately into glory, then for the saint on Earth, Christ and His Heaven are always only a few missed heart beats and missed breaths away.
Of course Christ in His Divine Nature is everywhere, and Christ by His Holy Spirit is even closer to us, dwelling in us in a special sense.
Even if Heaven is far away, in another part of the Universe, God can translate both bodies and souls there in an instant, as He did with Enoch, Elijah and, no doubt, Christ (Hebrews 11:5) Was Moses' body translated there, too (Jude)?
Man has only started exploring the Universe and there are many places in the Universe of which He does not know where they are.
There are three Heavens, as Austin mentioned, the Sky, Outer Space and the Heaven of Heavens. Does that indicate that the Heaven of Heavens is not in our Universe but in another dimension?
