The Bible teaches us about the Millennium and the White Throne Judgment. God tells us that our life in the Kingdom of God will be eternal and the Kingdom will last forever (Isaiah 9:6-7, Luke 1:31-33). God also describes for us the New Jerusalem that God will dwell in on the earth (Revelation 21:1-4).
The Bible doesn't give us much information about what we will be doing in the eternity that follows. We know it will be joyous (Psalm 16:11).
It is as if God gives us descriptions of the Millennium, the White Throne Judgment period, and the New Jerusalem as an example of the kind of happiness and accomplishment we will enjoy for eternity.
God has allowed scientists in our time to discover many things about the universe. Scientists make mistakes, and some of the things they teach are wrong, but one thing I think they are right about is the vastness of the physical universe. The universe is much greater than is needed simply to provide the view we have of the sky with the sun, moon, and stars visible to our eyes. At most we can see a few thousand stars with our naked eyes. But there is much more than that.
The stars we see are suns, similar to our sun, very far away, and each can have planets orbiting around them, some perhaps similar in size and composition to our earth. Most of the stars we see are in the Milky Way galaxy as we are, and there are many galaxies. Scientists estimate there are perhaps about 100-200 billion stars in our galaxy and there are perhaps 100-200 billion galaxies in the known universe.
I want to speculate a little about what the Family of God might be doing after the White Throne Judgment.
Eternity is a difficult concept for the human mind to grasp, so I have chosen to consider only a tiny slice of time, a mere fraction of a second compared to eternity, a small period of time that our limited human minds can more easily grasp. Thus the title of this post, "The First 500 Trillion Years". That is easier to understand than infinity.
God is creator, and He is the author of life and beauty. The life that exists on earth in all its variety is testimony to that. It is likely that God will lead His Family to create life on other planets in this vast universe.
Christ may begin by teaching us in detail about the chemistry of life, the DNA code, and how to design and create new forms of life, giving us knowledge far beyond anything scientists presently know. Then perhaps we will start with the planets and moons in this solar system. Mars would need a richer atmosphere and might need to be closer to the sun. Venus has too much atmosphere and the wrong kind and may need to be farther from the sun. The gas giants have moons that may be able to be modified to support life. Christ may organize us into teams to work with these planets, creating life, and managing the ecology.
Once we have done that with the solar system, we may go out to do the same with all the solar systems in the galaxy, and after that, the same for all the galaxies.
There are enough stars in our galaxy for each one with multiple planets filled with life to be ruled and managed by one person born into God's family in the Millennium or White Throne Judgment. And after this, there are enough galaxies for each son of God to rule and manage an entire galaxy. God will see to it that we have the powers of mind and Spirit to fulfill our responsibilities. Our minds and our powers will be vastly increased beyond what we have today.
Those in the Church today, the first fruits, those in the first resurrection, will have the priviledge of dwelling in the New Jerusalem, the headquarters of the universe, with Christ Himself (Revelation 3:12-13, 21). He will share His joy with us (Matthew 25:21-23).
And through all this, the greatest joy will be the happy and loving fellowship and unity we enjoy with God the Father, Jesus Christ, all the saints, all those made sons of God and added to His family in the Millennium and White Throne Judgment, and all God's holy angels.
Here are links to related sections in Preaching the Gospel:
God's Purpose for Mankind, Chapter 2