The Bible never mentions other universes. It only describes God creating “the heavens and the earth” (Gen 1:1) and interacting with people on earth.
However, it does describe different heavens. In fact, the word “heaven” is used in several different ways: to start with, it can mean the atmosphere, outer space and where God dwells. See “What is the third heaven?” for a discussion of these uses and an explanation of 2 Corinthians 12:2.
The “heavens” are also used figuratively to mean the political leaders (those who are above everyone else) as distinct from “earth” (the people they rule). For example, this is how it is used in Haggai 2:21-22.
Speak to Zerubbabel, governor of Judah, saying, I am about to shake the heavens and the earth, and to overthrow the throne of kingdoms. I am about to destroy the strength of the kingdoms of the nations, and overthrow the chariots and their riders. And the horses and their riders shall go down, every one by the sword of his brother.
Here, “heavens and earth” refers to the governments and people of the day. The same symbolism is found in Isaiah’s description of the overthrow of Babylon in Isaiah 13:13,15. Because the Bible uses the word “heaven” in several different ways, we need to decide by context what the word means when it occurs.
“A new heaven and a new earth” is also used symbolically to mean a new order of things (God’s Kingdom) where the rulers and the people change. This is how it is used in Isaiah 65:17-19; 66:22; 2 Peter 3:13 and Revelation 21:1.