What is the origin of the belief that God will not destroy the world but use the current one?

What is the origin of the belief that God will not destroy the world but use the current one?

Thou shalt send forth thy spirit, and they shall be created: and thou shalt renew the face of the earth. - Psalm 104:30

St. Paul speaks to us a the whole of creation being compared to the pains as being in childbirth.

For we know that every creature groaneth and travaileth in pain, even till now. - Romans 8: 22

Fire is seen as a means of purification to renew or purify many things.

But the day of the Lord shall come as a thief, in which the heavens shall pass away with great violence, and the elements shall be melted with heat, and the earth and the works which are in it, shall be burnt up. - 2 Peter 3:10

Many of the Church Fathers believed the world will be consumed by fire, but that does not in itself exclude a renewal of the earth and the universe as we know it.

Yes, St. Peter saw the world will altered at the Last Judgement, but it does not exclude that it would or would not be used to simply renew the existing world as we know it.

But the heavens and the earth which are now, by the same word are kept in store, reserved unto fire against the day of judgment and perdition of the ungodly men. - 2 Peter 3:7

Unless I am misreading something, St. Thomas Aquinas in his Summa Theologiae tends to believe that the earth will be renewed rather than being destroyed and recreated. He deals with it in Question 91: The quality of the world after the judgment.

Whether the world will be renewed?

We believe all corporeal things to have been made for man's sake, wherefore all things are stated to be subject to him [Psalm 8:5, seqq.]. Now they serve man in two ways, first, as sustenance to his bodily life, secondly, as helping him to know God, inasmuch as man sees the invisible things of God by the things that are made (Romans 1:20). Accordingly glorified man will nowise need creatures to render him the first of these services, since his body will be altogether incorruptible, the Divine power effecting this through the soul which it will glorify immediately. Again man will not need the second service as to intellective knowledge, since by that knowledge he will see God immediately in His essence. The carnal eye, however, will be unable to attain to this vision of the Essence; wherefore that it may be fittingly comforted in the vision of God, it will see the Godhead in Its corporeal effects, wherein manifest proofs of the Divine majesty will appear, especially in Christ's flesh, and secondarily in the bodies of the blessed, and afterwards in all other bodies. Hence those bodies also will need to receive a greater inflow from the Divine goodness than now, not indeed so as to change their species, but so as to add a certain perfection of glory: and such will be the renewal of the world. Wherefore at the one same time, the world will be renewed, and man will be glorified.

Whether the movement of the heavenly bodies will cease?

There are three opinions touching this question. The first is of the philosophers who assert that the movement of the heaven will last for ever. But this is not in keeping with our faith, which holds that the elect are in a certain number preordained by God, so that the begetting of men will not last for ever, and for the same reason, neither will other things that are directed to the begetting of men, such as the movement of the heaven and the variations of the elements. Others say that the movement of the heaven will cease naturally. But this again is false, since every body that is moved naturally has a place wherein it rests naturally, whereto it is moved naturally, and whence it is not moved except by violence. Now no such place can be assigned to the heavenly body, since it is not more natural to the sun to move towards a point in the east than to move away from it, wherefore either its movement would not be altogether natural, or its movement would not naturally terminate in rest. Hence we must agree with others who say that the movement of the heaven will cease at this renewal of the world, not indeed by any natural cause, but as a result of the will of God. For the body in question, like other bodies, was made to serve man in the two ways above mentioned (Article 1): and hereafter in the state of glory man will no longer need one of these services, that namely in respect of which the heavenly bodies serve man for the sustenance of his bodily life. Now in this way the heavenly bodies serve man by their movement, in so far as by the heavenly movement the human race is multiplied, plants and animals needful for man's use generated, and the temperature of the atmosphere rendered conducive to health. Therefore the movement of the heavenly body will cease as soon as man is glorified.

Whether the brightness of the heavenly bodies will be increased at this renewal?

The renewal of the world is directed to the end that, after this renewal has taken place, God may become visible to man by signs so manifest as to be perceived as it were by his senses. Now creatures lead to the knowledge of God chiefly by their comeliness and beauty, which show forth the wisdom of their Maker and Governor; wherefore it is written (Wisdom 13:5): "By the greatness of the beauty and of the creature, the Creator of them may be seen, so as to be known thereby." And the beauty of the heavenly bodies consists chiefly in light; wherefore it is written (Sirach 43:10): "The glory of the stars is the beauty of heaven, the Lord enlighteneth the world on high." Hence the heavenly bodies will be bettered, especially as regards their brightness. But to what degree and in what way this betterment will take place is known to Him alone Who will bring it about.

Whether the elements will be renewed by an addition of brightness?

Just as there is a certain order between the heavenly spirits and the earthly or human spirits, so is there an order between heavenly bodies and earthly bodies. Since then the corporeal creature was made for the sake of the spiritual and is ruled thereby, it follows that corporeal things are dealt with similarly to spiritual things. Now in this final consummation of things the lower spirits will receive the properties of the higher spirits, because men will be as the angels in heaven (Matthew 22:30): and this will be accomplished by conferring the highest degree of perfection on that in which the human spirit agrees with the angelic. Wherefore, in like manner, since the lower bodies do not agree with the heavenly bodies except in the nature of light and transparency (De Anima ii), it follows that the lower bodies are to be perfected chiefly as regards brightness. Hence all the elements will be clothed with a certain brightness, not equally, however, but according to their mode: for it is said that the earth on its outward surface will be as transparent as glass, water as crystal, the air as heaven, fire as the lights of heaven.